please explain the steps:
Jim Williamson began a 96-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 4 miles per hour and rides at 20 miles per hour, find the amount of time he spent on the bicycle.
time on bike = t hrs
time walking = 9-t hrs
distance on bike = 20t miles
distance walking = 4(9-t) mile
20t + 4(9-t) = 96
solve for t
To find the amount of time Jim spent on the bicycle, we need to use the formula: time = distance / speed.
Step 1: Calculate the distance Jim walked.
Since the whole trip was 96 miles, and he walked the entire distance, the distance he walked is equal to 96 miles.
Step 2: Calculate the time Jim spent walking.
His walking speed is 4 miles per hour, and the distance he walked is 96 miles.
Using the formula: time = distance / speed, we can calculate the time Jim spent walking:
time = 96 miles / 4 miles per hour = 24 hours.
However, we need to take into account that the total trip took 6 hours, so we know that Jim didn't spend the whole 24 hours walking.
Step 3: Subtract the time Jim spent walking from the total trip time.
Total trip time - Walk time = Bike time
6 hours - 24 hours = -18 hours
Since it doesn't make sense for the bike time to be negative, we know that Jim didn't spend any time on the bike.
So, the amount of time Jim spent on the bicycle is 0 hours.