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A bicyclist riding against the wind averages 10 miles per hour in traveling from A to B, but with the wind averages 15 miles per hour  in returning from B to A. How many miles per hour is his average speed for the trip?

 May 4, 2020
 #1
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Here is my solution:

 

Let a = The average speed for the trip
Let d = The one-way distance

Next we Write a time equation: time = distance/speed
 

Against time + with time = total time

d/15 + d/10 + 2d/a


Then we multiply by 30a
2a(d) + 3a(d) = 30(2d)
2ad + 3ad = 60d
5ad = 60d
divide both sides by d
5a = 60
a = 60/5
a = 12 mph is the average speed for the trip
 

coolsmileycool

 May 4, 2020
 #2
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D/10 = T................(1)

D/15 = T - 1/3.........(2)
When he cycles @ 15mph, that means it is going to take him 10/15 =2/3 of the time of cycling @ 10 mph. 
Solve (1) and (2) above and you will get:
D = 10 miles
T = 1 hour

[2*10] / [1+2/3] =20 x 3/5 =12 mph - his average speed.

 May 5, 2020

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