Jim began a 146-mile bicycle trip to build up stamina for a triathlete 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 40 miles per hour, find the amount of time he spent on the bicycle.

3.5 hours

Step-by-step explanation:

Let us represent

The time spent walking as x

The time spent riding as y

Jim began a 146-mile bicycle trip to build up stamina for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 5 hours.

Hence:

x + y = 5 Equation 1

x = 5 - y

If Jim walks at a rate of 4 miles per hour and rides at 40 miles per hour,

The formula for Distance = Speed × time. Hence,

4 × x + 40 × y = 146 miles

4x + 40y = 146 Equation 2

We substitute 5 - y for x in Equation 2

4(5 - y) + 40y = 146

20 - 4y + 40y = 146

Subtract 20 from both sides

20 - 20 - 4y + 40y = 146 - 20

- 4y + 40y = 146 - 20

36y = 126

y = 126/36

y = 3.5 hours

Since the time he spent raiding his bicycle is represented by "y", the amount of time he spent on the bicycle is 3.5 hours