Jim began a 207 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 6 hours. If Jim walks at the rate of 3 miles per hour and rides 45 miles per hour, find the amount of time he spent on the bicycle
w + r = 6 ... 3 w + 3 r = 18
3 w + 45 r = 207
subtract equations to eliminate w
To find the amount of time Jim spent on the bicycle, we can use the information given about his overall trip and the speeds at which he walks and rides.
Let's assume that Jim spent x hours cycling and (6 - x) hours walking.
According to the given information:
- Jim rides at a speed of 45 miles per hour.
- Jim walks at a speed of 3 miles per hour.
Using the formula: distance = speed × time, we can calculate the distances traveled by Jim during each part of the trip.
The distance covered while cycling is given by:
distance cycled = speed cycled × time cycled
distance cycled = 45 × x
The distance covered while walking is given by:
distance walked = speed walked × time walked
distance walked = 3 × (6 - x)
Since Jim's total trip distance is 207 miles, we can write the equation:
distance cycled + distance walked = 207
Substituting the expressions for distance cycled and distance walked, we have:
45x + 3(6 - x) = 207
Simplifying the equation:
45x + 18 - 3x = 207
42x + 18 = 207
42x = 207 - 18
42x = 189
Dividing both sides of the equation by 42:
x = 189 / 42
x = 4.5
So Jim spent 4.5 hours cycling.
Therefore, Jim spent 4.5 hours on the bicycle during his trip.