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

Answer:

7 miles and 6 miles respectively.

Step-by-step explanation:

For me,

Distance = 0.5 miles,

Time = 3 minutes,

So, pace = $\frac{Time}{Distance}$ = $\frac{3}{0.5}$ = 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 = $\frac{14}{2}$ = 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 = $\frac{Distance}{Time}$

$=\frac{0.5}{3}$

$=\frac{1}{6}$ miles per minute,

Similarly my friend's speed = $\frac{2}{14}$ = $\frac{1}{7}$ miles per minute,

In 42 minutes,

Distance covered by me = $\frac{1}{6}\times 42$ = 7 miles,

Distance covered by my friend = $\frac{1}{7}\times 42$ = 6 miles.