Jim began a 121-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 6 hours. If Jim walks at a rate of 5 miles per hour and rides at 31 miles per hour, find the amount of time he spent on the bicycle.

Question

Jim began a 121-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 6 hours. If Jim walks at a rate of 5 miles per hour and rides at 31 miles per hour, find the amount of time he spent on the bicycle.

Answer 1

ride for time t

walk for time (6-t)

31 t + 5(6-t) = 121
31 t + 30 - 5 t = 121
26 t = 91
t = 3.5 hours on bike
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check
3.5 * 31 + 2.5 * 5 = ?

Answer 2

Let's assume that Jim spent x hours on his bicycle.

During the time he was riding, he traveled at a speed of 31 miles per hour. So, the distance covered while riding is 31x miles.

Since the total trip length is 121 miles, the distance covered while walking can be calculated as 121 - 31x miles.

Now, let's calculate the time spent walking. We know that Jim walks at a rate of 5 miles per hour. So, the time spent walking is (121 - 31x) / 5 hours.

The total time for the trip is given as 6 hours. Therefore, the equation can be written as:

x + (121 - 31x) / 5 = 6

To solve this equation, we can multiply through by 5 to remove the fraction:

5x + 121 - 31x = 30

Combining like terms:

-26x + 121 = 30

Subtracting 121 from both sides:

-26x = -91

Dividing by -26:

x = -91 / -26

Simplifying:

x = 3.5

Therefore, Jim spent 3.5 hours on the bicycle.

Answer 3

To find the amount of time Jim spent on the bicycle, we can set up an equation using the given information.

Let's assume that Jim spent "x" hours riding his bicycle and the remaining time, which is 6 - x, walking.

Since speed is equal to distance divided by time, we can calculate the distances Jim covered riding and walking.

The distance covered riding is equal to his riding speed multiplied by the time he spent riding: 31 * x.
The distance covered walking is equal to his walking speed multiplied by the time he spent walking: 5 * (6 - x).

Since the total distance covered is 121 miles, we can sum the distances and set it equal to 121: 31x + 5(6 - x) = 121.

Simplifying the equation:
31x + 30 - 5x = 121
26x + 30 = 121
26x = 91
x = 91 / 26
x ≈ 3.5

Therefore, Jim spent approximately 3.5 hours on the bicycle.