Problema Solution

Joe leaves school going 14mph on his bike.

Three hours later Sam leaves going 54mph.

How far does Joe travel before Sam catches up to him?

Answer provided by our tutors

let


t1 = the time of Joe's travel

v1 = 14 mph the speed of Joe

v2 = 54 mph the speed of Sam

t2 = the time of Sam's travel


Since Sam leaves the school 3 hours later we have


t2 = t1 - 3


the distance of Joe's travel = the distance of Sam's travel


t1*v1 = t2*v2


we are using the formula for speed = distance/time that is v = d / t => d = v*t


14*t1 = 54*t2


by solving the system of equations


t2 = t1 - 3

14*t1 = 54*t2


we find


t1 = 81/20 = 4.05 hours


t2 = 20/21 = 1.05 hours


we need to calculate the distance that Joe travels


t1*v1 = 4.05*14 = 56.7 miles


Joe will make 56.7 miles trip before Sam catches him up.