SOLUTION: A bicyclist bikes the 24 mi to a city averaging a certain speed. The return trip is made at a speed that is 4 mph slower. The total time for the round trip is 5 hr. Find the b
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-> SOLUTION: A bicyclist bikes the 24 mi to a city averaging a certain speed. The return trip is made at a speed that is 4 mph slower. The total time for the round trip is 5 hr. Find the b
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Question 1194434: A bicyclist bikes the 24 mi to a city averaging a certain speed. The return trip is made at a speed that is 4 mph slower. The total time for the round trip is 5 hr. Find the bicyclist's average speed on each part of the trip. Answer by greenestamps(13198) (Show Source):
Get some good mental exercise by solving the problem informally.
The distance is a whole number, the total time is a whole number, and the difference in speeds is a whole number. So the two speeds are almost certain to be whole numbers.
So look for two speeds that are whole numbers of miles per hour that differ by 4 and for which the total time going 24 miles and returning is 5 hours. A little trial and error should quickly find speeds of 12 and 8 mph: .
ANSWERS: 12mph going; 8mph returning
With formal algebra....
Let x be his speed going
Then x-4 is his speed returning
The total time for 24 miles each way is 5 hours:
Multiply by the common denominator, x(x-4):
or
x=8/5 makes no sense, since it would make the return trip at a negative speed; so x=12.
