SOLUTION: The rate of the bicyclist is 7 mph faster than the rate of a long-distance runner. The bicyclist travels 30 miles in the same amount of time that the runner travles 16 miles. Find

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Question 123539: The rate of the bicyclist is 7 mph faster than the rate of a long-distance runner. The bicyclist travels 30 miles in the same amount of time that the runner travles 16 miles. Find the rate of the runner.
I know you can find rate R= d/t i have 30/x+7 for cyclist and 16/x for runner. I don't know what to do with these numbers now.
Please help
THANK you
Answer by stanbon(48558) About Me  (Show Source):
You can put this solution on YOUR website!
The rate of the bicyclist is 7 mph faster than the rate of a long-distance runner.
The bicyclist travels 30 miles in the same amount of time that the runner travles 16 miles.
Find the rate of the runner.
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Bicyclist DATA:
Distance = 30 miles ; Rate = x+7 mph ; Time = d/r = 30/(x+7) hrs.
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Runner DATA:
Distance = 16 miles ; Rate = x mph ; Time = d/r = 16/x hrs
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EQUATION:
cyclist time = runner time
30/(x+7) = 16/x
30x = 16x+112
14x = 112
x = 8 mph (runner rate)
===========================
Cheers,
Stan H.