SOLUTION: A car travels for 100 miles at a uniform speed. If speed is increased by 5 miles per hour, the trip would take one hour less time. What are the original speeds?

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Question 1108152: A car travels for 100 miles at a uniform speed. If speed is increased by 5 miles per hour, the trip would take one hour less time. What are the original speeds?
Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.
100%2Fr - 100%2F%28r%2B5%29 = 1   is your time equation  (two fractions are values of time spent under each scenario)

where "r" is the unknown rate under the question.


To solve it, multiply both sides by r*(r+5). You will get


100*(r+5) - 100r = r*(r+5)

100r + 500 - 100r = r^2 + 5r

r^2 + 5r - 500 = 0.

(r-20)*(r+25) = 0.


Only the positive root r = 20  makes sense.


Answer.  The rate under the question is 20 miles per hour.