The cost of an adult ticket to a football game was 1.75. The cost of a student ticket 1.25. The number of student tickets sold was twice the number of adult tickets. The total income from the sale of tickets was 850. How many tickets of each type were sold?

Answer:

proud of you keep ya head up

Step-by-step explanation:

Answer:

[tex]t=\frac{32.5-30}{\frac{30}{\sqrt{225}}}=1.25[/tex]    

[tex]p_v =P(t_{(224)}>1.25)=0.106[/tex]  

If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can't conclude that the true mean is actually its significantly higher than 30.

Step-by-step explanation:

Data given and notation  

[tex]\bar X=32.5[/tex] represent the sample mean  

[tex]s=30[/tex] represent the sample standard deviation

[tex]n=225[/tex] sample size  

[tex]\mu_o =30[/tex] represent the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean exceeds 30, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 30[/tex]  

Alternative hypothesis:[tex]\mu > 30[/tex]  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]t=\frac{32.5-30}{\frac{30}{\sqrt{225}}}=1.25[/tex]    

P-value

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=225-1=224[/tex]  

Since is a one side rigth tailed test the p value would be:  

[tex]p_v =P(t_{(224)}>1.25)=0.106[/tex]  

Conclusion  

If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can't conclude that the true mean is actually its significantly higher than 30.  

Frank is incorrect because both fractions are not same.

Step-by-step explanation:

We have to compare both fractions in their simplest forms to compare them

Given

Baseball cards in Missy's Collection:    [tex]\frac{3}{4}[/tex]

Baseball cards in Frank's Collection:  [tex]\frac{8}{12}[/tex]

Converting the fraction in simplest form will give us:

[tex]\frac{2}{3}[/tex]

Both the fractions are not same as one is 3/4 and one is 2/3.

Hence,

Frank is incorrect

Keywords: Fractions, decimals

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Answer:

x = 27.2.

Step-by-step explanation:

As BD || CE   the triangles ABD and ACE are similar.

AB = 25 - 8 = 17.

AB / AC = AD / AE     ( similar triangles)

17 / 25 = x / 40

x = 17*40 / 25

= 27.2.

Answer:

d. 32 π

Step-by-step explanation:

As given

Area of circle = 64 π

Area of circumference = 1/2*(Area of circle)

Area of circumference = 1/2*(64π)

Area of circumference = 0.5*64π

Area of circumference = 32π

A circle is a curve sketched out by a point moving in a plane. The correct option is A, 12π unit.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.

Given that the area of the circle is less than 64π. Therefor, the area of the circle can be written as,

Area of the circle < 64π units²

πR² < 64π

R < 8 units

Now, the circumference of the circle should be less than the circumference of the circle having radius of 8 units. Therefore, we can write,

Circumference of the circle with radius R < Circumference of the circle with radius of 8 units

2πR < 2 × π × 8 units

2πR < 16π units

Therefore, from the above inequality the circumference of the circle should be less than 16π unit. Since the only feasible option is 12π.

Hence, the correct option is A, 12π unit.

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Answer:

[tex]12x+3\leq 27[/tex]

Step-by-step explanation:

It is given that

[tex]9\geq4x+1[/tex]

We need to find the possible range of values of 12x+3.

Subtract -1 from both sides.

[tex]9-1\geq 4x[/tex]

[tex]8\geq 4x[/tex]

Multiply both sides by 3.

[tex]24\geq 12x[/tex]

Add 3 on both sides.

[tex]24+3\geq 12x+3[/tex]

[tex]27\geq 12x+3[/tex]

It can be rewritten as

[tex]12x+3\leq 27[/tex]

Therefore, 12x+3 must be less than or equal to 27.

Answer:

The probability for a girl to be born is 0.4913. This technique doesnt appear to improve the likelihood of having a baby girl.

Step-by-step explanation:

Since the number of babies selected for this technique, using the law of big numbers, we conclude that the proportion of babies that are girls in the selection is approximately equal than the probability for a girl to be selected. Thus, the probability that a girl will be born using the technique is 281/(281+291) = 0.4913.

Since in general girls are slightly more likely to be born than boys, then we can conclude that the technique doesnt have an effect in improving the likelihood of having a baby girl, but the opposite.

Answer:

The answer to your question is B. (1.5, -6)

Step-by-step explanation:

Data

A (8, -3)

B (-5, -9)

Formula

Xm = [tex]\frac{x1 + x2}{2}[/tex]

Ym = [tex]\frac{y1 + y2}{2}[/tex]

Substitution

x1 = 8    x2 = -5

                     Xm = [tex]\frac{8 - 5}{2} = \frac{3}{2}[/tex]

y1 = -3   y2 = -9

                     Ym = [tex]\frac{-3 - 9}{2} = \frac{-12}{2} = -6[/tex]

Midpoint = (3/2, -6) = (1.5, -6)

Answer:

Step-by-step explanation:

1)

[tex]4m+5=\dfrac{3m-5}{2} \quad\text{given}\\\\2(4m+5)=\dfrac{2(3m-5)}{2} \quad\text{multiply by 2}\\\\8m+10=3m-5 \quad\text{use the distributive property}\\\\(8m+10)-(3m+10)=(3m-5)-(3m+10) \quad\text{subtract $3m+10$}\\\\5m=-15 \quad\text{collect terms}\\\\\dfrac{5m}{5}=\dfrac{-15}{5} \quad\text{divide by 5}\\\\m=-3 \quad\text{simplify}[/tex]

____

2)

[tex]-2+7(x+2)=5(2x-2)+4 \quad\text{given}\\\\-2+7x+14=10x-10+4 \quad\text{use the distributive property}\\\\7x+12=10x-6 \quad\text{collect terms}\\\\(7x+12)-(7x-6)=(10x-6)-(7x-6) \quad\text{subtract $7x-6$}\\\\18=3x \quad\text{collect terms}\\\\\dfrac{18}{3}=\dfrac{3x}{3} \quad\text{divide by 3}\\\\6=x \quad\text{simplify}[/tex]

Answer:

The 13 students on floor

Step-by-step explanation:

The sample is a portion of population selected to view the aspects of population as whole population is difficult to follow. Here, the sample is 13 students on the floor because it is selected from 22 students on the floor.

The population consists of 22 students on floor and 13 out of 20 is the sample because it is a portion of population.

Answer:

1750 + 35x ≥ 3250

Step-by-step explanation:

Average speed = 35 words

He has already typed 1500 words on his final paper

The paper must be more than 3250 words.

To find at least how many more words he has to type, we will subtract 1500 from 3250

3250 - 1500 = 1750 words

The equation will be 35x ≥ 1750

x is the number of minutes

The equation could be

1750 + 35x ≥ 3250

Answer:

Option B. Range of the given sample data is 113.

Step-by-step explanation:

The given question is incomplete; here is the complete question.

Find the range for the given sample data.

The amounts below represent the last twelve transactions made to Juan's checking account.  Positive numbers represent deposits and negative numbers represent debits from his account.

$28   -$20   $67   -$22   -$15   $17  -$38  $41   $53   -$13   $30   $75

Option A. $75

Option B. $113

Option C. $37

Option D. -$113

Transaction done by Juan can be arrange from lowest to highest

-38   -22   -20    - 15    -13    17   28    30   41   53    67    75    

Now we know rage of the sample data = Highest value - Lowest value

= 75 - (-38)

= 113

Therefore, range of the given sample data is 113.

Option B is the answer.

Answer:

48.6625 before rounding, I'm sure the instruction told you where it preferred you to round.

Step-by-step explanation:

1. Convert percent value to a decimal.

The way to do this is by moving the period at 15.00 two places to the left.

2. Now that you have the decimal .15, multiply it by Mrs. King's subtotal (57.25).

you should get 8.5875.

3. Subtract the discount amnt. (8.5875) from the subtotal (57.25).

You should get 48.6625.

Answer:$920

Step-by-step explanation:

Since the variation is joint, I=KPr where k is the constant of proportionality.

Plugging in the values of I=$375, P=$1500 and r=5% in the equation I=KPr, the value of k can be calculated. Hence, the formula connecting the three quantities (I,P and r) can be generated.

375 = K (1500×5)

Making k the subject of change,

K = 375/(1500×5)

K=1/20

Formula connecting the three quantities :I =Pr/20

when P=$2300, r=8%,

I = (2300×8)/20

I = $920

Answer:

A.

Step-by-step explanation:

Probability sampling means that each unit in population has an equal chance or probability of selection in a sample.

Cluster sampling is a probability sampling method because population is divided into clusters at random and no personal judgement is involved. Thus, each cluster has equal probability of selecting and sampling is done as random. Hence, cluster sampling is a probability sampling method.

Cluster sampling is a probability sampling method. Here option A is correct.

It involves dividing the population into clusters or groups based on certain characteristics, such as geographical location or other relevant attributes. Then, a random sample of clusters is chosen, and all individuals within those selected clusters become part of the sample.

This method is considered probabilistic because each cluster has a known probability of being selected, and thus each individual within the chosen clusters has a chance of being included in the sample. This makes it possible to estimate population parameters and make statistical inferences.

Cluster sampling differs from other probability sampling methods, such as simple random sampling, in that it involves a multi-stage process.

It is particularly useful when it's impractical or too costly to gather a complete list of all individuals in the population, making it a valuable tool in various fields of research, including public health, sociology, and economics. Here option A is correct.

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Answer:

88

Step-by-step explanation:

9 pages

Each holds 9

He has 7 more

81+7=88

Answer: 35 granola bars and 45 pies were sold.

Step-by-step explanation:

Let x represent the number of granola bar that was sold.

Let y represent the number of pie that was sold.

A school marching band will raise one dollar for each granola bar and five dollars for each pie they sell. Yesterday, they raise $260 by selling 80 bars and pies.

This means that

x + 5y = 260 - - - - - - - - - -1

Since they sold a total of 80 bars and pies, it means that

x + y = 80

Substituting x = 80 - y into equation 1, it becomes

80 - y + 5y = 260

- y + 5y = 260 - 80

4y = 180

y = 180/4 = 45

x = 80 - y = 80 - 45

x = 35

Answer:

Megan has left with $24.

Step-by-step explanation:

Let the total money she has be 'y'.

Given:

Megan spent two out of five of her money on a doll.

So we can say that;

Money spent on doll = [tex]\frac{2}{5}y[/tex]

Also Given:

half of the remainder on a musical box.

Money spent on musical box = [tex](y-\frac{2}{5}y)\frac{1}2[/tex]

Now we will make the denominator common using LCM we get;

Money spent on musical box =[tex](\frac{5y}{5}-\frac{2y}{5})\times\frac{1}2}=(\frac{5y-2y}{5})\times \frac{1}{2}=\frac{3y}{10}[/tex]

Now Given:

she spent eight dollars more on the doll than on a musical box.

[tex]\frac{2y}{5} = \frac{3y}{10}+8[/tex]

Combining like terms we get;

[tex]\frac{2y}{5}-\frac{3y}{10}=8[/tex]

Now we will make the denominator common using LCM we get;

[tex]\frac{2y\times2}{5\times2}-\frac{3y}{10}=8\\\\\frac{4y}{10}-\frac{3y}{10}=8\\\\\frac{4y-3y}{10}=8\\\\y=8\times10\\\\y=\$80[/tex]

Money spent on doll = [tex]\frac{2}{5}y=\frac{2}{5}\times 80 = \$32[/tex]

she spent eight dollars more on the doll than on a musical box.

So we can say that;

Money spent on musical box = Money spent on doll -8 = [tex]32-8 = \$24[/tex]

Now to find the remaining money left we will subtract Money spent on doll and Money spent on musical box from total money she had.

framing in equation form we get;

remaining money left = [tex]80-32-24= \$24[/tex]

Hence Megan has left with $24.

Answer:

A. 30 and 3.4641

Step-by-step explanation:

The solution is Option A.

The value of the standard deviation is given by μx = 30 and σx = 3.4641

The standard deviation of a statistic's sample distribution, or an approximation of that standard deviation, is the statistic's standard error. The standard error of the mean is used when referring to a statistic that is the sample mean. The standard error of the mean, or simply standard error, indicates how different the population mean is likely to be from a sample mean.

The standard error S = √ [ ( 1 - p ) p / n ]

where p = population proportion

n = sample size

Given data ,

Let the number of trials n = 50

Let the probability of success be represented as p = 0.60

Now , let the standard deviation be σ

S = √ [ ( 1 - p ) p / n ]

Substituting the values in the equation , we get

S = √ ( 0.60 ) ( 0.40 ) / 50

S = √ 0.24/50

S = √0.0048

S = 0.0692820

So , the value of σ = 0.0692820

Therefore , the value of σx = 0.0692820 x 50 = 3.4641

Now , the value of μx = 0.60 x 50 = 30

Hence , the value of μx and σx are 30 and 3.4641 respectively

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Answer:

That the government did not defend the rights of the Indians.

Step-by-step explanation:

Sand Creek, Colorado was the place where hundreds of Cheyenes and Arapahoes were massacred by the Colorado Territory militia, which terrorized indigenous peoples to abandon their lands.

Answer: +$45

Step-by-step explanation: if his actual pay for the week was $100 then from the question he incorrectly calculated it as {$100 + $45} = $145 which is $45 above his actual pay.

Error = measured value - actual

value.

= $145 -$100 =$45.

NOTE: since the value he assumed{$145} is greater than his actual pay{$100}, we have to include a positive sign to the error{$45}.

Therefore, Error = +$45.

Ray's error was incorrectly calculating his additional pay as $45 instead of the correct amount of $90. To find the correct overtime pay, we need to determine how many hours Ray worked in excess of his regular hours and the rate at which he receives overtime pay.

The error Ray made when calculating his overtime pay was incorrectly calculating the additional pay. To find the correct overtime pay, we need to determine how many hours Ray worked in excess of his regular hours and the rate at which he receives overtime pay. Let's assume that Ray receives time-and-a-half for overtime work.

Therefore, Ray's error was incorrectly calculating his additional pay as $45 instead of the correct amount of $90.

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Final answer:

To find the possible values of b in the equation 2a + b = 15.7 in an isosceles triangle, we can assume different values for a and solve for b. Two lengths that make sense for possible values of b are 5.7 and 3.7.

Explanation:

To determine which lengths make sense for possible values of b in the equation 2a + b = 15.7, we need to consider the fact that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Since the triangle is isosceles, two sides have the same length, which is represented by a. Let's assume that a = 5 (one possible value) and substitute it into the equation: 2(5) + b = 15.7. Solving for b, we get b = 5.7. This means that a possible value for b is 5.7. Another option is when a = 6, which gives us b = 3.7. Therefore, the two lengths that make sense for possible values of b are 5.7 and 3.7.

Answer:

The simplified expression is:

⇒ [tex]13x-8[/tex]

Step-by-step explanation:

Given expression:

[tex](9x + \frac{1}{2})+(4x-8\frac{1}{2})[/tex]

To simplify the given expression.

Solution:

In order to simplify, we will combine the like terms by removing the parenthesis.

We have:

⇒  [tex]9x + \frac{1}{2}+4x-8\frac{1}{2}[/tex]

Combining like terms.

⇒  [tex]9x+4x+\frac{1}{2}-8\frac{1}{2}[/tex]

⇒  [tex]13x+\frac{1}{2}-8\frac{1}{2}[/tex]

In order to combine fractions, we will combine the whole number and the fraction separately.

⇒  [tex]13x-8+(\frac{1}{2}-\frac{1}{2})[/tex]

⇒  [tex]13x-8+0[/tex]

Thus, the simplified expression is:

⇒ [tex]13x-8[/tex]

Answer:

The broker's commission was rupees 8,250

Step-by-step explanation:

Selling price of property = rupees 450,000

The sale price is higher than rupees 300,000

Commission for rupees 300,000 = 2% × rupees 300,000 = rupees 6,000

Remaining amount = rupees 450,000 - rupees 300,000 = rupees 150,000

Commission for the remaining amount = 1.5% × rupees 150,000 = 0.015 × rupees 150,000 = rupees 2,250

Total commission = rupees 6,000 + rupees 2,250 = rupees 8,250

Answer:

They have [tex]9\frac{3}{6}\ cups[/tex] of flour altogether.

Step-by-step explanation:

Given:

Amount of flour Javon has = [tex]\frac{3}{2}\ cup[/tex]

Amount of flour Sam has = [tex]4\frac{1}{3}\ cups[/tex]

[tex]4\frac{1}{3}\ cups[/tex] can be Rewritten as [tex]\frac{13}{3}\ cups[/tex]

Amount of flour Sam has = [tex]\frac{13}{3}\ cups[/tex]

Amount of flour Antoine has = [tex]3\frac{4}{6}\ cups[/tex]

[tex]3\frac{4}{6}\ cups[/tex] can Rewritten as [tex]\frac{22}{6}\ cups[/tex]

Amount of flour Antoine has = [tex]\frac{22}{6}\ cups[/tex]

We need to find the amount of cups of flour they have altogether.

Solution:

Now we can say that;

the amount of cups of flour they have altogether can be calculated by sum of Amount of flour Javon has and Amount of flour Sam has and Amount of flour Antoine has.

framing in equation form we get;

amount of cups of flour they have altogether = [tex]\frac{3}{2}+\frac{13}{3}+\frac{22}{6}[/tex]

Now to solve we need to make the denominator common by using L.C.M we get;

amount of cups of flour they have altogether = [tex]\frac{3\times3}{2\times3}+\frac{13\times2}{3\times2}+\frac{22\times1}{6\times1}=\frac{9}{6}+\frac{26}{6}+\frac{22}{6}[/tex]

Now Denominators are common so we will add the numerators we get;

amount of cups of flour they have altogether = [tex]\frac{9+26+22}{6}= \frac{57}{6}\ cups\ \ OR \ \ 9\frac{3}{6}\ cups[/tex]

Hence They have [tex]9\frac{3}{6}\ cups[/tex] of flour altogether.

Answer:

[tex]r=\frac{2(23146)-(139)(333)}{\sqrt{[2(9661) -(139)^2][2(55457) -(333)^2]}}=1[/tex]

So then the we have perfect linear association.  Because the heights and weights of the men are similar.

Step-by-step explanation:

Let X represent the Height and Y the weigth

We have the follwoing dataset:

X: 70, 69

Y: 169, 164

n=2

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.  

And in order to calculate the correlation coefficient we can use this formula:  

[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]  

For our case we have this:  

n=2 [tex] \sum x = 139, \sum y = 333, \sum xy = 23146, \sum x^2 =9661, \sum y^2 =55457[/tex]  

And if we replace in the formula we got:

[tex]r=\frac{2(23146)-(139)(333)}{\sqrt{[2(9661) -(139)^2][2(55457) -(333)^2]}}=1[/tex]

So then the we have perfect linear association.  Because the heights and weights of the men are similar.

Answer:

a=7.2*1.5=10.8 cm

b=6.3/1.5=4.2 cm

[tex]\pounds 4.48*2.25=\pounds 10.08[/tex]

Step-by-step explanation:

Proportional Geometric Shapes

A) We are given two similar shapes of a logo. They are to be proportional. We only need to find the proportion ratio of two of them to find the rest of the lengths.

The upper sides have 7.5 cm and 5 cm respectively. This gives us the ratio

[tex]\displaystyle r=\frac{7.5}{5}=1.5[/tex]

Which means all the measures of the smaller logo are 1.5 smaller than those of the larger. This means  

b=6.3/1.5=4.2 cm

a=7.2*1.5=10.8 cm

B) To paint the logos, we need to cover its surface, so the ratio of the surface is 1.5*1.5=2.25

This means the cost to paint the larger logo is  

[tex]\pounds 4.48*2.25=\pounds 10.08[/tex]

Answer:

A) a = 10.8, b = 4.2

B) £10.08

Step-by-step explanation:

A) 7.5/5 = 1.5

a = 7.2 x 1.5 = 10.8

5/7.5 = 2/3

b = 6.3 x 2/3 = 4.2

B) 1.5 x 1.5 = 2.25

£4.48 x 2.25 = £10.08

Answer:

It would be correct to conclude that approximately 68 percent of the scores would fall between 85 and 115.          

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 100

Standard Deviation, σ = 15

We are given that the distribution is a bell shaped distribution that is a normal distribution.

Empirical rule

Thus, approximately 68% of data will lie within one standard deviation of mean.

[tex]\mu - \sigma = 100-15 = 85\\\mu + \sigma = 100 + 15 = 115[/tex]

Thus, it would be correct to conclude that approximately 68 percent of the scores would fall between 85 and 115.

68 percent of the scores would fall between 85 and 115.

Empirical rule states that for a normal distribution, about 68% are within one standard deviation from the mean, 95% are within two standard deviation from the mean and 99.7% are within three standard deviation from the mean.

Given that mean(μ) = 100 and standard deviation (σ) = 15

68 percent of the scores would fall between μ ± σ = 100 ± 15 = 85, 115

68 percent of the scores would fall between 85 and 115.

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Answer:

56

Step-by-step explanation:

z varies jointly with x and y:

z = kxy

When x = 2 and y = 2, z = 7.

7 = k(2)(2)

k = 7/4

z = 7/4 xy

When x = 4 and y = 8:

z = 7/4 (4)(8)

z = 56

Answer:

Speed of first train = 36 mph

Speed of second train =  60 mph

Step-by-step explanation:

Given:

First train leaves Cincinnati at 2:00 PM

Second train leaves same station at 4:00 PM

Speed of second train is 24 mph faster than first train.

The second train overtakes the first at 7:00 PM

To find the speeds of each train.

Solution:

First train:

Let speed of first train be = [tex]x\ mph[/tex]

Time of travel between 2:00 PM to 7:00 PM = [tex]7-2=5\ h[/tex]

Distance traveled by 1st train in 5 hours in miles = [tex]Speed\times time = x\times 5 = 5x[/tex]

Second train:

Then, speed of second train will be = [tex](x+24)\ mph[/tex]

Time of travel between 4:00 PM to 7:00 PM =[tex]7-4 = 3\ h[/tex]

Distance traveled by second train in 3 hours in miles = [tex]Speed\times time = (x+24)\times 3=3x+72[/tex]

At 7:00 PM both trains meet as the second train overtakes the first. This means the distance traveled by both the trains is same at 7:00 PM as they both leave from same stations.

Thus, we have:

[tex]5x=3x+72[/tex]

Solving for [tex]x[/tex]

Subtracting both sides by [tex]3x[/tex]

[tex]5x-3x=3x-3x+72[/tex]

[tex]2x=72[/tex]

Dividing both sides by 2.

[tex]\frac{2x}{2}=\frac{72}{2}[/tex]

∴ [tex]x=36[/tex]

Speed of first train = 36 mph

Speed of second train = [tex]36+24=[/tex] 60 mph

Final answer:

The speed of the first train is 36 mph and the speed of the second train, which is 24 mph faster, is 60 mph. This was determined by setting up an equation based on the equal distances covered by both trains when the second overtakes the first.

Explanation:

The question involves solving a rate, time, and distance problem typically found in algebra or kinematics. To find the speeds of the two trains, we can set up an equation based on the fact that the distance covered by both trains is the same at the point where the second train overtakes the first. Let's define the speed of the first train as s (in mph). Therefore, the speed of the second train will be s + 24 mph. Since the first train leaves at 2:00 pm and is overtaken at 7:00 pm, it travels for 5 hours. The second train, leaving two hours later at 4:00 pm, travels for 3 hours.

The distance covered by each train can be expressed as their speed multiplied by the time traveled. For the first train, it's s 5 hours, and for the second train, it's (s + 24) 3 hours. Setting these two distances equal gives us:

s 5 = (s + 24)  imes 3

Solving for s gives:

s  imes 5 = 3s + 72
5s - 3s = 72
2s = 72
s = 36

So, the speed of the first train is 36 mph, and the speed of the second train is 60 mph (36 + 24).