SOLUTION: Two hoses, when connected to a swimming pool,can fill the pool together in 4 hours. If the larger hose alone is used, it can fill the pool in 6 hours less than the smaller hose. Ho
Question 1095687: Two hoses, when connected to a swimming pool,can fill the pool together in 4 hours. If the larger hose alone is used, it can fill the pool in 6 hours less than the smaller hose. How long will it take the smaller hose to fill the swimming pool alone? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Two hoses, when connected to a swimming pool, can fill the pool together in 4 hours.
If the larger hose alone is used, it can fill the pool in 6 hours less than the smaller hose.
How long will it take the smaller hose to fill the swimming pool alone?
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Let s = time required by the small hose to fill the pool alone
then
(s-6) = time required by the large hose
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Let the completed job = 1 (a full pool)
:
Each hose does a fraction of the job, the two fractions add up to 1 = = 1
multiply equation by s(s-6)
s(s-6)* = s(s-6)* = 1s(s-6)
Cancel the denominators and you have
4s + 4(s-6) = s^2 - 6s
4s + 4s - 24 = s^2 - 6s
8s - 24= s^2 - 6s
arrange as a quadratic equation
0 = s^2 - 6s - 8s + 24
s^2 - 14s + 24 = 0
Factors to
(s-12)(s-2) = 0
two solutions
s = 2
and the reasonable solution
s = 12 hrs is time required to fill the pool with the small hose
:
the large hose takes 6 hrs less, therefore
6 hrs is the time required by the large hose
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:
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See if that checks out + =
reduce fractions + = 1
