Question

you and a friend are running on treadmills you run 0.5 miles every 3 minutes and your friend runs 2 miles every 14 minutes. you both start and stop running at the same time and run a whole number of miles. what is the least possible number of miles you and your friend can run?

Answer 1

7 miles and 6 miles respectively.

Explanation:

For me,

Distance = 0.5 miles,

Time = 3 minutes,

So, pace =
`(Time)/(Distance)` =
`(3)/(0.5)` = 6 minute per miles,

That is, I am running 1 mile in 6 minutes.

For my friend,

Distance = 2 miles,

Time = 14 minutes,

So, pace =
`(14)/(2)` = 14 minutes per mile,

That is, my friend is running 1 mile in 7 minutes,

Thus, the time after we will meet = LCM(6,7) = 42 minutes,

Also, my speed =
`(Distance)/(Time)`

`=(0.5)/(3)`

`=(1)/(6)` miles per minute,

Similarly my friend's speed =
`(2)/(14)` =
`(1)/(7)` miles per minute,

In 42 minutes,

Distance covered by me =
`(1)/(6)* 42` = 7 miles,

Distance covered by my friend =
`(1)/(7)* 42` = 6 miles.