Question

A long distance runner starts at the beginning of a trail and runs at a rate of 6 miles per hour. Two hours later, a cyclist starts at the beginning of the trail and travels at a rate of 16 miles per hour. What is the amount of time that the cyclist travels before overtaking the runner?

Answer 1

the time for the bike = x
the time for the runner = x+2 ( started 2 hours before bike)

runners speed = 6, bike speed = 16

so you have 6(x+2) = 16x

distribute the left side:

6x +12 = 16x

subtract 6x from each side:

12 = 10x

divide both sides by 10
x = 12/10
x = 1.2 hours

1 hour = 60 minutes
1.2 x 60 = 72 minutes