Question

Great ran a one mile race in 5 minutes. Inex ran a quarter mile in 1 minute and 20 seconds.

If Inez ran the mile at her quarter mile pace of 1 minute and 20 seconds, how fast would she run the mile? Write your answer in minutes and seconds. (There are 4 quarter miles in a one mile race). 1._______)
2. Which of the two runners had the fastest time? ______

3. How much faster was her mile in seconds? _______

Answer 1

1. The time it would take Inex to run 1 mile is 5 minutes 20 seconds

2. Great has the fastest (lowest) time

3. When running a mile Great is faster than Inex by 20 seconds

Explanation:

1. The distance Great ran in 5 minutes = 1 mile

The distance Inex ran in 1 minute and 20 seconds = A quarte mile = (1/4) mile

We note that 1 minute and 20 seconds = 4/3 minutes

Given that the time Inex ran 1/4 mile = 4/3 minutes...(1)

We have;

The time it would take Inex to run 1 mile is given as follows;

1 = (1/4) ÷ (1/4)

1 mile = ((1/4) ÷ (1/4)) mile = (1/4) mile/(1/4)

The time to run 1 mile = The time to run (1/4) mile/(1/4) = 4/3 minutes/(1/4) (by dividing both sides of equation (1) by (1/4),

4/3 minutes/(1/4) = 4 × 4/3 minutes = 16/3 minutes =
`5(1)/(3)` minutes= 5 minutes 20 seconds

The time it would take Inex to run 1 mile = 5 minutes 20 seconds

2. Given that Great ran a one mile race in 5 minutes, and Inex ran the same one mile race in 1 minute and 20 seconds, Great has the fastest (lowest) time

3. The amount faster Great's time is faster than Inex's time to run one mile = 5 minute 20 seconds - 5 minutes = 20 seconds.