SOLUTION: To train for a marathon, Mei runs an 18-mile course at constant speed. If she doubles her usual speed, she can compete the course in an hour and a half less than her usual time. Wh

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Question 408347: To train for a marathon, Mei runs an 18-mile course at constant speed. If she doubles her usual speed, she can compete the course in an hour and a half less than her usual time. What is Mei's usual speed and her usual time to compete the course
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Mei runs an 18-mile course at constant speed.
If she doubles her usual speed, she can compete the course in an hour and a half less than her usual time.
What is Mei's usual speed and her usual time to compete the course?
:
Change 1 hr and a half to 1.5 hrs
:
Let s = the normal speed
then
2s = double the normal speed
:
Write a time equation, Time = dist/speed
:
Usual time - faster time = 1.5 hrs
18%2Fs - 18%2F%282s%29 = 1.5
multiply by 2s to clear denominators, results:
2(18) - 18 = 2s(1.5)
36 - 18 = 3s
18 = 3s
s = 18%2F3
s = 6 mph is the usual speed
:
Find the usual time
18%2F3 = 3 hrs is the usual time
:
:
Check solution by finding the time at the faster speed (12 mph)
18%2F12 = 1.5 hrs, which is 1.5 hrs faster than the usual time of 3 hrs