SOLUTION: Working togather, two pipes can fill one tankin 4 hours. Working alone the smaller pipe would take 6 hours longer than the smaller pipe to fill the tank. How many hours would it ta
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Question 588924: Working togather, two pipes can fill one tankin 4 hours. Working alone the smaller pipe would take 6 hours longer than the smaller pipe to fill the tank. How many hours would it take the larger pipe th fill the tank, working alone?
Please help if can, and have time to do so. thank you Jason
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Working together, two pipes can fill one tank in 4 hours.
Rewrite this so it makes sense.
Working alone the smaller pipe would take 6 hours longer than the larger pipe to fill the tank
How many hours would it take the larger pipe the fill the tank, working alone?
'
let x = time required by the larger pipe alone
then
(x+6) = time required by the smaller pipe alone
:
Let the completed job = 1 (a full tank)
:
Each pipe does a fraction of the job. The two fraction add up to 1
:
Large pipe = small pipe = a full tank
+ = 1
multiply by x(x+6)
x(x+6)* + x(x+6)* = x(x+6)
cancel the denominators and you have
4(x+6) + 4x = x(x+6)
4x + 24 + 4x = x^2 + 6x
8x + 24 = x^2 + 6x
combine on the right
0 = x^2 + 6x - 8x - 24
a quadratic equation
x^2 -2x - 24 = 0
Factors to
(x-6)(x+4) = 0
the positive solution
x = 6 hrs, the large pipe alone
;
:
See if this checks out. (Small pipe will take 12 hrs alone)
+ =
+ = 1; confirms our solution
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