SOLUTION: Marco’s speed riding up a hill is 40% of his speed riding down the hill. It takes him two hours longer to ride up the hill than it takes him to ride down the hill. How long, in hou

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Question 316801: Marco’s speed riding up a hill is 40% of his speed riding down the hill. It takes him two hours longer to ride up the hill than it takes him to ride down the hill. How long, in hours, does it take him to ride down the hill? Express your answer as a common fraction.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Marco’s speed riding up a hill is 40% of his speed riding down the hill.
It takes him two hours longer to ride up the hill than it takes him to ride down the hill.
How long, in hours, does it take him to ride down the hill?
Express your answer as a common fraction.
:
Let s = his speed down hill
then
.4s = his speed up hill
:
Let one way distance = 10
:
Write a time equation: time = dist/speed
:
Time up - time down = 2 hrs
10%2F.4s - 10%2Fs = 2 hrs
multiply by .4s, results
10 - .4(10) = 2(.4s)
:
10 - 4 = .8s
:
6 = .8s
s = 6%2F.8
s = 7.5 is the downhill speed
then
.4(7.5) = 3 is the uphill speed
:
Find the time to ride down hill
10/7.5 = 11%2F3 hr
:
Check solution by finding the time uphill
10/3 = 31%2F3 hr, a two hr difference