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) (Show Source):
- = 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.