# college algebra

posted by .

Solve the problem. A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time for the trip was 5 hours. If his rate when he was riding a bicycle was 10 miles per hour faster than his rate walking, what was each rate?

• college algebra -

let walking rate be x mph
let biking rate be x+10

time for walking = 12/x
time biking = 8/(x+10)

isn't 12/x + 8(x+10) = 5 ?

multiply each term by x(x+10)
you will get quadratic, solve for x

• college algebra -

Let the walking speed be v and the bike speed V = v + 10.
12/(v+10) + 8/v = 5 is the sum of the times spent bidking and walking.

Solve that equation for v. You will have to start with a common denominator.
[12v + 8(v+10)]/[v(v+10)] = 5
5 v^2 + 50 v = 20 v + 80
v^2 + 6v - 16 = 0
(v + 8)(v -2) = 0
Choose the positive root, v = 2 miles/hr
The bike speed was then v + 10 = 12 mph.

• college algebra -

go with drwls solution, I mixed up the two rates.

• college algebra -

Solve. V^2-6v-16=0

## Similar Questions

1. ### MATH

Rate Problem: Mr. Stewart rode a distance of 12miles out into the country on a bicycle and returned on foot. His rate on the bicycle was 4 times his rate on foot. He spent 5 hours on the entire trip. Find the rate of walking and on …
2. ### intermediate algebra

You can travel 40 miles on a motorcycle in the same time that it takes to travel 15 miles on a bicycle. If your motorcycle's rate is 20 miles per hour faster than your bicycle's rate, find the speed of the motorcycle and bicycle. motorcycle …
3. ### Math

Joseph rode his bicycle for 10 miles. Then he increased his speed to an average of 15 miles per hour for the next h hours. Write an equation for the total distance he rode. thanks in advance!
4. ### math

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 …
5. ### math

jim began a 131 mile bicycle trip to build up stamina for a triathlete competetion.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 …
6. ### Math

Greg rode his bicycle at a constant speed of 20 miles per hour. Plot points on the graph to represents the distances Greg rode after 1, 2, 3, and 4 hours (1 hour= 20 miles, 2 hours= 40 miles, 3 hours= 60 miles, 4 hours= 80 hours) Then …
7. ### Math

Greg rode his bicycle at a constant speed of 20 miles per hour. Plot points on the graph to present the distances Greg rode after 1,2,3, and 4 hours (1 hour = 20 miles, 2 hours = 40, 3 hours = 60, 4 hours = 80 miles). Write an equation …
8. ### ALGEBRA

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 …
9. ### math

amara rode her bicycle 8 miles in 0.5 hours.what was the average rate that she rode her bicycle in miles per hour?
10. ### algebra

Justin rode his bicycle to a park located 4 2/3 miles from his house.he returned along the same route. After riding 9 1/8 miles total, how many more miles does justin need to ride to reach his home?

More Similar Questions