jim began a 92-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 4 hours. If Jim walks at a rate of 3 miles per hour and rides at 35 miles per hour, find the amount of time he spent on the bicycle.
Spent X hrs. on bike.
Spent 4-X hrs. walking.
35x + 3(4-x) = 92.
X = ?.
4-x = ?.
since time = distance/speed, if he rode for x miles, then
x/35 + (92-x)/3 = 4
x = 87.5 miles
now you can find the time he spent riding.
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.
Since the total trip took 4 hours, the time spent walking can be found by subtracting "x" from 4. So the time spent walking is (4 - x) hours.
Now, to calculate the distance traveled by each mode of transportation, we can use the formula:
distance = rate * time
For the bike ride, the distance can be calculated as:
distance(bike ride) = rate(bike ride) * time(bike ride)
distance(bike ride) = 35 mph * x
For the walk, the distance can be calculated as:
distance(walk) = rate(walk) * time(walk)
distance(walk) = 3 mph * (4 - x)
According to the problem, the total distance traveled is 92 miles. So we can set up the equation:
distance(bike ride) + distance(walk) = total distance
35x + 3(4 - x) = 92
Now we can solve this equation for "x" to find the amount of time Jim spent on the bicycle.
35x + 12 - 3x = 92
32x = 80
x = 2.5
Therefore, Jim spent 2.5 hours on the bicycle.
let b equal distance on bicycle
(b / 35) + [(92 - b) / 5] = 4 ... solve for b
time on bicycle = b / 35