You run one lap around a mile track every 8 minutes. your friend runs around the same track every 10 minutes. you both start at the starting line at the same time. how far have each of you run the next time you meet at the starting line

I ran 10 miles and my friend ran 8 miles.

Step-by-step explanation:

Given,

The time taken by me to cover one lap = 8 minutes,

While, the time taken by my friend to cover one lap = 10 minutes,

∵ 8 = 2 × 2 × 2, 10 = 2 × 5

Thus, LCM(8, 10) = 2 × 2 × 2 × 5 = 40

If me and my friend started at the same point,

Hence, the time after which we will first time = LCM( 8, 10)

= 40 minutes.

Also, one lap = 1 miles,

Thus, when we meet first time,

The distance covered by me = = 5 miles,

The distance covered by my friend = = 4 miles,

Therefore,

When we meet next time,

The distance covered by me = 2 × 5 = 10 miles,

The distance covered by my friend = 2 × 4 = 8 miles.