SOLUTION: Natasha rides her bike (at a constant speed) for 4 hours, helped by a 24) wind of 3 miles per hour. Pedaling at the same rate, the trip back against the wind takes 10 hours. Find

Question 1164012: Natasha rides her bike (at a constant speed) for 4 hours, helped by a 24) wind of 3 miles per hour. Pedaling at the same rate, the trip back against
the wind takes 10 hours. Find the total round trip distance she
traveled.
Found 3 solutions by solver91311, greenestamps, MathTherapy:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

The distance traveled at some rate plus three miles per hour for four hours is the same as the distance traveled at the same rate minus three miles per hour, so:

Solve for , then calculate

John

My calculator said it, I believe it, that settles it

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Her rates are r+3 with the wind and r-3 against the wind.

The ratio of times to go the same distance is 4:10 = 2:5, so the ratio of speeds is 5:2.

Solve using basic algebra

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Natasha rides her bike (at a constant speed) for 4 hours, helped by a 24) wind of 3 miles per hour. Pedaling at the same rate, the trip back against
the wind takes 10 hours. Find the total round trip distance she
traveled.

Let distance be D, and average speed, without the wind, be S
Then we get the following OUTGOING-SPEED equation:
Also, the RETURN-SPEED equation is:
------ Substituting for S in eq (ii)

2D = 5D - 120 ----- Multiplying by LCD, 20
2D - 5D = - 120
- 3D = - 120
Distance she traveled, one way, or
Round-trip distance: .
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