SOLUTION: A cyclist does an out-and-back summit ride. The cyclist averaged 10 mph on the way out and 20 mph on the way back. What was the cyclists average speed for the entire ride? A cyc

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Question 706091: A cyclist does an out-and-back summit ride. The cyclist averaged 10 mph on the way out and 20 mph on the way back. What was the cyclists average speed for the entire ride?
A cyclist is on an out-and-back summit ride. The cyclist averaged 10 mph on the way out and wants to average 20 mph for the entire ride. What speed must the cyclist average on the way back to reach this goal?

*I would love to get a detailed answered. I'm very confused by these problems and can't seem to get them right*
Answer by josgarithmetic(39633) About Me  (Show Source):
You can put this solution on YOUR website!
Explaining this seems hard, but I am able, with thought, to SEE how to handle the first part.

First, we do not have specific facts on the time or distance, but we know that way-out and way-back are equal distances. Average speed will be total distance divided by sum of time for the whole trip, out and back.

Trip Part__________speed_____________time_____________distance
way out____________10________________d/10_____________d
way back___________20________________d/20_____________d

total distance = 2d
total time = d/10 + d/20

Average Speed Entire Trip = 2d%2F%28%28d%2F10%29%2B%28d%2F20%29%29
Do the Arithmetic, algebraic steps.