Algebra 1 Word Problem

Question

Jim began a 130​-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 5 hours. If Jim walks at a rate of 5 miles per hour and rides at 35 miles per​ hour, find the amount of time he spent on the bicycle.

Answer 1

Total Distance: 130 m

Total Time: 5 h

Speeds: 5 mph when walking and 35 mph on bicycle

Out of 5 hours spent on the trip, a portion of time is spent while bicycling and the remaining is spent walking. If 't' is the time spent bicycling, then (5-t) is the time spent walking. (Notice how I picked 't' to be the time spent bicycling because that is what the question asked and now I have to figure out the value for 't')

So if we break the trip into 2 portions, one portion for cycling and the other for walking, we could write expressions for distances for each portion of the trip.

Since Distance = speed x time

Distance while cycling = (35) x (t) = 35t

Distance while walking = (5) x (5-t) = 5(5-t) = 25 - 5t

We know that total distance is the sum of distances while cycling and while walking and that total distance is given in the question to be 130 miles. We can therefore write the following equation

(35t) + (25 - 5t) = 130

We can now solve for t. Recall that t is the time spent bicycling as per our assumption at the start and this is what is being asked in the question.

35t + 25 - 5t = 130

=> t = 3.5 h

So this means that 3.5 h of the trip was spent bicycling.

Answer 2

w + b = 5

w = 5 - b

D_b = 35b

D_w = 5w

D_b + D_w = 130

35b + 5w = 130

35b + 5(5 - b) = 130

Can you solve for b and answer?