SOLUTION: need help with this word problem:
shelly can cut a lawn with a riding mower in 5 hours less time than it takes William to cut a lawn with a push mower, if they can cut the lawn
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-> SOLUTION: need help with this word problem:
shelly can cut a lawn with a riding mower in 5 hours less time than it takes William to cut a lawn with a push mower, if they can cut the lawn
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Question 299667: need help with this word problem:
shelly can cut a lawn with a riding mower in 5 hours less time than it takes William to cut a lawn with a push mower, if they can cut the lawn in 2 hours working together find how long to the nearest tenth of an hour it takes for William to cut the lawn alone. Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! shelly can cut a lawn with a riding mower in 5 hours less time than it takes William to cut a lawn with a push mower, if they can cut the lawn in 2 hours working together find how long to the nearest tenth of an hour it takes for William to cut the lawn alone.
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Let w = time it takes for William to cut lawn alone
then
w-5 = time it takes Shelly to cut
.
2(1/w + 1/(w-5)) = 1
multiplying both sides by: w(w-5)
2((w-5) + w) = w(w-5)
2(2w-5) = w(w-5)
4w-10 = w^2-5w
-10 = w^2-9w
0 = w^2-9w+10
Apply the quadratic formula to yield:
w = {7.7, 1.3}
Throw out the 1.3 answer (extraneous) leaving us with:
w = 7.7 hours
.
Details of quadratic formula to follow:
