Question

5.) students at albion middle school are given a fitness test. the results of their tests are shown in the table. use the table to answer the questions a - c.
fitness test result
evan: $1\frac{1}{2}$ miles in 15 minutes
toby: $\frac{2}{3}$ miles in 6 minutes
jillian: $\frac{3}{4}$ miles in 9 minutes
a) find the time it takes each student to run 1 mile. show your work.
evan:
toby:
jillian:
b) which student is running at the fastest rate?

c) jillian is trying out for the cross country team. to make the team, she must run $3\frac{1}{2}$ miles in less than 36 minutes. will jillian make the team?
show your work.

Explanation:

Part (a)

Evan:

Step1: Identify distance and time

Evan runs \(1\frac{1}{2}=\frac{3}{2}\) miles in 15 minutes.

Step2: Calculate time per mile

To find time per mile, divide time by distance: \(15\div\frac{3}{2}=15\times\frac{2}{3}=10\) minutes per mile.

Toby:

Step1: Identify distance and time

Toby runs \(\frac{2}{3}\) miles in 6 minutes.

Step2: Calculate time per mile

Divide time by distance: \(6\div\frac{2}{3}=6\times\frac{3}{2}=9\) minutes per mile.

Jillian:

Step1: Identify distance and time

Jillian runs \(\frac{3}{4}\) miles in 9 minutes.

Step2: Calculate time per mile

Divide time by distance: \(9\div\frac{3}{4}=9\times\frac{4}{3}=12\) minutes per mile.

Part (b)

Answer:

Step1: Find Jillian's rate

From part (a), Jillian takes 12 minutes per mile.

Step2: Calculate time for \(3\frac{1}{2}=\frac{7}{2}\) miles

Time = \(12\times\frac{7}{2}=42\) minutes.

Step3: Compare with 36 minutes

42 minutes > 36 minutes, so she won't make the team.

Final Answers:

a) Evan: 10 minutes, Toby: 9 minutes, Jillian: 12 minutes
b) Toby
c) No, Jillian will not make the team.