Question

Students at Polk middle school are given a fitness test the results of their test are show. In the table below Evian 1 1/2 miles in 15 minutes Toby 2/3 miles in 6 minutes Jillian 3/4 miles in 9 minutes

Answer 1

a. It takes Evian
`\( (1)/(10) \)` of a mile per minute to run.

b. Toby is running at the fastest rate, as
`\( (1)/(9) \)` is the largest value among the three.

c. Jillian would take 42 minutes to run 3 1/2 miles. Since this is less than the required time of 40 minutes, Jillian will make the team.

How did we get these values?

Given in the table that:

Evian: 1 1/2 miles in 15 minutes

Toby: 2/3 miles in 6 minutes

Jillian: 3/4 miles in 9 minutes

a. Find the time it takes each student to run 1 mile:

To find the time it takes to run 1 mile for each student, we can use the following formula:

`\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]`

a. Evian:

`\[ \text{Speed} = (1 (1)/(2))/(15) \]`

`\[ \text{Speed} = (3)/(2) / 15 \]`

`\[ \text{Speed} = (1)/(10) \]`

So, it takes Evian
`\( (1)/(10) \)` of a mile per minute to run.

b. Toby:

`\[ \text{Speed} = (2)/(3) / 6 \]`

`\[ \text{Speed} = (1)/(9) \]`

So, it takes Toby
`\( (1)/(9) \)` of a mile per minute to run.

c. Jillian:

`\[ \text{Speed} = (3)/(4) / 9 \]`

`\[ \text{Speed} = (1)/(12) \]`

So, it takes Jillian
`\( (1)/(12) \)` of a mile per minute to run.

b. Which student is running at the fastest rate? Explain:

Comparing the speeds, Evian runs at
`\( (1)/(10) \)` of a mile per minute, Toby runs at
`\( (1)/(9) \)` of a mile per minute, and Jillian runs at
`\( (1)/(12) \)` of a mile per minute.

Therefore, Toby is running at the fastest rate, as
`\( (1)/(9) \)` is the largest value among the three.

c. Jillian is trying out for the cross country team. To make the team, she must run 3 1/2 miles in less than 40 minutes. Will Jillian make the team? Explain:

Jillian's speed is
`\( (1)/(12) \)` of a mile per minute. To find out if she can make the team, we can calculate the time it would take her to run 3 1/2 miles:

`\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]`

`\[ \text{Time} = (7)/(2) / (1)/(12) \]`

`\[ \text{Time} = (7)/(2) * (12)/(1) \]`

`\[ \text{Time} = 42 \]`

Jillian would take 42 minutes to run 3 1/2 miles. Since this is less than the required time of 40 minutes, Jillian will make the team.

Complete question:

Students at Polk middle school are given a fitness test the results of their test are show. In the table below: Evian 1 1/2 miles in 15 minutes Toby 2/3 miles in 6 minutes Jillian 3/4 miles in 9 minutes.

a. Find the time it takes each student to run 1 mile. Evian:_ Toby:_ Jillian:_ b. Which student is running at the fastest rate? Explain.

c. Jillian is trying out for the cross country team. To make the team, she must run 3 1/2 miles in less than 40 minutes. Will Jillian make the team? Explain.