SOLUTION: Two pipes can together fill a tank in 40/13 mins. If one pipe takes 3 mins more than the other to fill it, find the timein which each pipe can fill the tank.
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Question 670601: Two pipes can together fill a tank in 40/13 mins. If one pipe takes 3 mins more than the other to fill it, find the timein which each pipe can fill the tank. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Two pipes can together fill a tank in 40/13 mins.
If one pipe takes 3 mins more than the other to fill it,
find the time in which each pipe can fill the tank.
:
let x = time for the other pipe to fill it
then
(x+3) = time for one pipe to fill it
:
Let the completed job = 1 (a full tank)
: + = 1
multiply by x(x+3), resulting in (x+3) + x = x(x+3)
multiply each term by 13, to get rid of those annoying denominators at last
40(x+3) + 40x = 13x(x+3)
:
40x + 120 + 40x = 13x^2 + 39x
Combine as a quadratic equation on the right
0 = 13x^2 + 39x - 80x - 120
13x^2 - 41x - 120 - 0
you can use the quadratic formula here, but this will factor to:
(13x+24)(x-5) = 0
the positive solution
x = 5 min for the other pipe
and
5 + 3 = 8 min for one pipe.
:
:
We can check this using the decimal equiv of 40/13; 3.077.
3.077/5 + 3.077/8 =
.6154 + .384625 = 1.000
