SOLUTION: Francis builds a fish pond for his fishes, goldfishes and a variety of carp. He decided to use two different hoses to easily fill his fish pond with water. Using together the two h
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Question 1171188: Francis builds a fish pond for his fishes, goldfishes and a variety of carp. He decided to use two different hoses to easily fill his fish pond with water. Using together the two hoses, it takes him 12 minutes to fill the fishpond. If he used one hose, he would be able to fill the pond 10 minutes faster than the other hose. How long does it take for each hose to fill the fish pond by itself? Answer by ikleyn(52776) (Show Source):
You can put this solution on YOUR website! .
Francis builds a fish pond for his fishes, goldfishes and a variety of carp. He decided to use two different hoses
to easily fill his fish pond with water. Using together the two hoses, it takes him 12 minutes to fill the fishpond.
If he used one hose, he would be able to fill the pond 10 minutes faster than the other hose.
How long does it take for each hose to fill the fish pond by itself?
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Let x = the unknown time for "one" hose, in minutes.
then the time for the "other" hose is ((x+10) minutes.
The individual rates of filling are of the tank volume per minute (for "one" hose)
and of the tank volume per minute (for the "other" hose).
The combined rate of filling is of the tank volume.
So, your balance equation is
+ = . (*)
To solve it, multiply both sides by 12*x*(x+10). You will get
12(x+10) + 12x = x*(x+10).
Simplify it step by step
12x + 120 + 12x = x^2 + 10x
x^2 - 14x - 120 = 0.
(x-20)*(x+6) = 0.
The roots are x= 20 and x= -6.
Of the two roots, only positive x= 20 is meaningful and makes sense.
ANSWER. "One" hose needs 20 minutes. The "other" hose needs 20+10 = 30 minutes.
CHECK. I will check if the equation (*) is valid.
+ = + = = . ! Correct !
