Jim began a 153-mile bicycle trip to build up stamina for a triathlon competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 5 hours. If Jim walks at a rate of 4 miles per hour and rides at 42 miles per hour, find the amount of time he spent on the bicycle.

consider the motion when Jim travels by bicycle

D = total distance to be traveled for the trip = 153 mile

v = speed of riding = 42 mph

t = time taken to complete the trip by bicycle = ?

using the equation

t = D / v

inserting the values

t = 153/42

t = 3.64 h

while walking and riding:

T = total time taken to complete the trip by walking and riding = 5 hours

t ' = time of walking = T - t = 5 - 3.64 = 1.36 hours

v' = speed of walking = 4 mph

d' = distance traveled by walking = ?

distance traveled by walking is given as

d' = v' t'

d' = 4 x 1.36

d' = 5.44 miles

d = distance traveled by bicycle = D - d' = 153 - 5.44 = 147.56 miles

v = speed of riding = 42 mph

t = time spent on the bicycle = ?

time spent on the bicycle is given as

t = d/v

t = 147.56/42

t = 3.51 hours