SOLUTION: hello please help me to solve this,thankyou!! two hoses, when connected to a swimming pool, can fill the pool in 4 hours. If the larger hose alone is used, it can fill the pool in

Algebra ->  Equations -> SOLUTION: hello please help me to solve this,thankyou!! two hoses, when connected to a swimming pool, can fill the pool in 4 hours. If the larger hose alone is used, it can fill the pool in      Log On


   

Question 1197446: hello please help me to solve this,thankyou!!
two hoses, when connected to a swimming pool, can fill the pool 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?
Found 3 solutions by MathLover1, josgarithmetic, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

We let the time taken when ....
the larger hose alone is used be+%28x+-+6%29
and the smaller hose as x.
This would make their rates and respectively.
Take note that:
1%2Frate+=+time+
so,
1%2Frate of both hoses = 4
rate of both hoses = 1%2F4

1%2F%28x-6%29%2B1%2Fx=1%2F4

%28x%2B%28x-6%29%29%2Fx%28x-6%29=1%2F4

%282x-6%29%2F%28x%5E2-6x%29=1%2F4

4%282x-6%29=1%28x%5E2-6x%29

8x-24=x%5E2-6x

0=x%5E2-6x-8x%2B24

0=x%5E2-14x%2B24

0=x%5E2-2x-12x%2B24

0=%28x%5E2-2x%29-%2812x-24%29

0=x%28x-2%29-12%28x-2%29

0=%28x-12%29%28x-2%29

This would mean that x+=+12 or x=2 but x+cannot be 2 since that would make the time taken for the larger hose negative.
Therefore it will take the smaller hose 12+hours to fill the swimming pool alone.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
                       TIME       RATE

smallhose                x       1/x

bighose                  x-6     1/(x-6)

combined                  4      1/4

Combined-rate
1%2Fx%2B1%2F%28x-6%29=1%2F4
-
x-6%2Bx=%28x%28x-6%29%29%2F4
2x-6=%28x%5E2-6x%29%2F4
8x-24=x%5E2-6x
x%5E2-14x%2B24=0
%28x-12%29%28x-2%29=0------------ x can only be 12.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

hello please help me to solve this,thankyou!!
two hoses, when connected to a swimming pool, can fill the pool 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 time the smaller hose takes be S
Then time the larger hose takes = S - 6
Since both, when turned on, fills it in 4 hours, we get: matrix%281%2C3%2C+1%2FS+%2B+1%2F%28S+-+6%29%2C+%22=%22%2C+1%2F4%29
                                                     4(S - 6) + 4S = S(S - 6) ------ Multiplying by LCD, 4S(S - 6)
                                                        
                                                                 0 = (S - 12)(S - 2)
                 
                 Time the smaller hose takes, working alone, or highlight_green%28matrix%281%2C4%2C+S%2C+%22=%22%2C+12%2C+hours%29%29       or        S = 2 hours (ignore)