SOLUTION: If a bicyclist is traveling 41 miles at a certain speed, the return speed is made 6 mph slower. The total time for the round trip is 15 hours. What is the average speed of the bicy

Question 1059912: If a bicyclist is traveling 41 miles at a certain speed, the return speed is made 6 mph slower. The total time for the round trip is 15 hours. What is the average speed of the bicyclist on the first trip?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x=speed
x*t=distance
x*t=41, so the outbound time is 41/x
(x-6)*t=41
t=41/(x-6), which is the inbound time.
Both times add to 15
41/x+{41/(x-6)}=15
Clear fractions by multiplying everything by x(x-6)
41(x-6)+41x=15x(x-6)
41x-246+41x=15x^2-90x
15x^2-172x+246=0
x=(1/30)(172+/-sqrt (172^2-60*246); sqrt 14824=121.75
x=(1/30)(293.75)=9.79 mph
x=(1/30)(50.25)=1.675 mph, and that can't work because x-6 would be negative

At 9.79 mph, it takes 4.19 hours outbound ANSWER 9.79 mph
At 3.79 mph, it takes 10.82 hours inbound
They add to 15.01, or 15 with rounding error.
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