SOLUTION: Two drain pipes can empty a pool in 17 1/2 minutes. The larger pipe can empty the pool in 12 minutes less than it would take the smaller pipe. How long will it take the smaller pip
Algebra ->
Rate-of-work-word-problems
-> SOLUTION: Two drain pipes can empty a pool in 17 1/2 minutes. The larger pipe can empty the pool in 12 minutes less than it would take the smaller pipe. How long will it take the smaller pip
Log On
Question 880394: Two drain pipes can empty a pool in 17 1/2 minutes. The larger pipe can empty the pool in 12 minutes less than it would take the smaller pipe. How long will it take the smaller pipe to empty the pool alone? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! let x = time required by the smaller pipe to drain the pool alone
then
(x-12) = time required by the larger pipe
let completed job = 1; (a drained pool)
:
Two drain pipes can empty a pool in 17 1/2 minutes.
The larger pipe can empty the pool in 12 minutes less than it would take the smaller pipe.
How long will it take the smaller pipe to empty the pool alone?
: + = 1
multiply equation by x(x-12),
x(x-12)* + x(x-12)* = x(x-12)
cancel the denominators and you have:
17.5(x-12) + 17.5x = x(x-12)
17.5x - 210 + 17.5x = x^2 - 12x
combine to form a quadratic equation on the right
0 = x^2 - 12x - 35x + 210
x^2 - 47x + 210 = 0
you can use the quadratic formula here, but this will factor to
(x-5)(x-42) = 0
two solutions
x = 5; not possible
and
x = 42 min for small pipe to empty the pool alone
:
:
See if that checks out. large pipe, 42 - 12 = 30 min =
.417 + .583 = 1
