Posted by **megan** on Wednesday, February 25, 2009 at 11:09am.

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 -
**Reiny**, Wednesday, February 25, 2009 at 12:44pm
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 -
**drwls**, Wednesday, February 25, 2009 at 12:49pm
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 -
**Reiny**, Wednesday, February 25, 2009 at 1:07pm
go with drwls solution, I mixed up the two rates.

- college algebra -
**Tim**, Sunday, July 31, 2011 at 11:19am
Solve. V^2-6v-16=0

## Answer this Question

## Related Questions

- Math - Joseph rode his bicycle for 10 miles. Then he increased his speed to an ...
- math - jim began a 131 mile bicycle trip to build up stamina for a triathlete ...
- math - please explain the steps: Jim Williamson began a 96-mile bicycle trip to ...
- MATH - Rate Problem: Mr. Stewart rode a distance of 12miles out into the country...
- Math - Brian rode his motorbike for 3 hours at 50 miles per hour and then rode ...
- Algebra - Norman traveled 261 miles on a trip to bates. The trip took 4 1/2 ...
- intermediate algebra - You can travel 40 miles on a motorcycle in the same time ...
- algebra - a two part canoe trip,the first part of the trip the canoist traveled...
- Algebra - The time required for a trip 108 miles downstream on a steamer is 3 ...
- Algebra. Please help(: - The time required for a trip 108 miles downstream on a ...