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?

Guest May 4, 2020

#1**+1 **

**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**

LuckyDucky May 4, 2020

#2**0 **

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.

Guest May 5, 2020