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?
:
Let s = time required by the small hose to fill the pool alone
then
(s-6) = time required by the large hose
:
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
:
:
:
See if that checks out
+ =
reduce fractions
+ = 1

RELATED QUESTIONS
hello please help me to solve this,thankyou!! two hoses, when connected to a swimming... (answered by MathLover1,josgarithmetic,MathTherapy)

When two hoses are connected to a swimming pool, they can fill the pool in 4 hrs if both... (answered by ikleyn)

A garden hose can fill a swimming pool in 4 days and a larger hose can fill the pool in... (answered by Theo)

With water from one hose, a swimming pool can be filled in 9 hours. A second, larger hose (answered by checkley77)

With water from one hose, a swimming pool can be filled in 7 hours. A second, larger hose (answered by Earlsdon,oberobic)

One hose can fill a small swimming pool in minutes. A larger hose can fill the pool in... (answered by Alan3354)

One hose can fill a small swimming pool in 70 minutes. A larger hose can fill the pool in (answered by nerdybill)

One hose can fill a small swimming pool in 50 minutes. A larger hose can fill the pool... (answered by htmentor)

One hose can fill a small swimming pool in 65 minutes. A larger hose can fill the... (answered by stanbon)