Problema Solution

Roger can run one mile in 8 minutes. Jeff can run one mile in 6 minutes. If Jeff gives Roger a 1 minute head​ start, how long will it take before Jeff catches up to​ Roger? How far will each have​ run?

Answer provided by our tutors

Let

v1 = 1/8 miles per min the average speed of Roger
v2 = 1/6 miles per min the average speed of Jeff
t = the time in minutes that Jeff runs before catches up to Roger
t + 1 = the time in minutes that Roger runs before Jess catches up with him

Since the both run the same distance and distance = speed*time we have:

v1*(t + 1) = v2*t

(1/8)(t + 1) = (1/6)*t

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t = 3 min

It will take 3 minutes for Jeff to catch up on Rogers.

The distance each of them runs is v2*t = (1/6)*3 = 1/2 mile or 0.5 miles.