Jim began a 281-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 7 hours. If Jim walks at a rate of 3 miles per hour and rides at 43 miles per hour, find the amount of time he spent on the bicycle.
To find the amount of time Jim spent on the bicycle, we can use the given information about his total trip time and the rates at which he walks and rides.
Let's assume that Jim spent x hours riding the bicycle. Since the total trip took 7 hours, the time spent walking can be calculated as 7 - x hours.
Now, let's find the distances covered in each mode of transportation. In x hours, Jim would cover a distance of 43 miles per hour * x hours = 43x miles on the bicycle. In 7 - x hours, Jim would cover a distance of 3 miles per hour * (7 - x) hours = 21 - 3x miles on foot.
Given that the total trip distance was 281 miles, we can set up the following equation:
43x + 21 - 3x = 281
Simplifying the equation:
40x + 21 = 281
40x = 260
x = 6.5
Therefore, Jim spent 6.5 hours riding the bicycle.
time = distance/speed, so if he rode x miles on the bike,
x/43 + (281-x)/3 = 7
solve for x, and then x/43 is the time on the bike.