SOLUTION: a hose needs 6 hours to fill a swimming pool. another hose needs 3 hours more to fill the pool then the 2 hoses combined. how long does it take the second hose to fill a swimming p

Algebra ->  Rate-of-work-word-problems -> SOLUTION: a hose needs 6 hours to fill a swimming pool. another hose needs 3 hours more to fill the pool then the 2 hoses combined. how long does it take the second hose to fill a swimming p      Log On


   

Question 945325: a hose needs 6 hours to fill a swimming pool. another hose needs 3 hours more to fill the pool then the 2 hoses combined. how long does it take the second hose to fill a swimming pool.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
(FOR THE EASIER SOLUTION METHOD, SEE THE ONE BELOW!)

Let x be time for "another hose" to fill the tank.
A hose, 1%2F6
Another hose, 1%2Fx
Two combined hoses, 1%2F6%2B1%2Fx=%28x%2B6%29%2F%286x%29


This seems unnatural to analyze:
the "Another hose needs 3 hours more to fill the pool then the 2 hoses combined. "

Best idea seems to try to compare the denominators for 1%2Fx and %28x%2B6%29%2F%286x%29 but this second expression must be used as a complex fraction with numerator of 1.

Combined hoses, 1%2F%28%28x6%29%2F%28x%2B6%29%29, meaning the time for combined hoses to fill the tank is 6x%2F%28x%2B6%29;
the description says that highlight%28x=3%2B%286x%29%2F%28x%2B6%29%29........


Reread and study the problem description and question; recheck my (incomplete) solution analysis , and think carefully about all parts. When you can make sense of it, then you can continue. Understanding this description and solution process here is far far far more important than getting the final result.



EASIER SOLUTION METHOD

x, time for another hose to fill tank
y, time for combined hoses to fill tank
-
RATES
A hose, 1%2F6
Another hose, 1%2Fx
Combined hoses, 1%2Fy
-
According to the given description, highlight_green%28x=3%2By%29.

Combined hoses rate,
1%2F6%2B1%2Fx=1%2Fy
x%2F%286x%29%2B6%2F%286x%29=1%2Fy
%28x%2B6%29%2F%286x%29=1%2Fy

Using the given description between x and y times, find highlight_green%28y=x-3%29;
Substitute this into the combined hoses rate...

highlight_green%28%28x%2B6%29%2F%286x%29=1%2F%28x-3%29%29
%28x%2B6%29%28x-3%29=6x
x%5E2%2B3x-18=6x
x%5E2-3x-18=0
which is factorable;
%28x%2B3%29%28x-6%29=0

The solution which makes meaningful sense is highlight%28x=6%29.
The "another hose" by itself will fill the tank in 6 hours.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

a hose needs 6 hours to fill a swimming pool. another hose needs 3 hours more to fill the pool then the 2 hoses combined. how long does it take the second hose to fill a swimming pool.
Time it takes 2nd hose, alone, to fill pool: highlight_green%286%29 hours

You can do the check!! 

===================

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