SOLUTION: A tank that hold 400 gallon of water can be filed by one pipe in 15 minutes and emptied by another pipe in 40 minutes. how mush time does it take to fill tank if both pipes are ope

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Question 1042396: A tank that hold 400 gallon of water can be filed by one pipe in 15 minutes and emptied by another pipe in 40 minutes. how mush time does it take to fill tank if both pipes are open?
Found 3 solutions by josgarithmetic, josmiceli, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The one tank can serve as the unit of volume. The filling or emptying rate is the sum of the two rates, INCLUDING SIGN.

Flow rate will be 1%2F15-1%2F40%29%28TANK%2FMINUTES%29.
The question is how many MINUTES to fill 1 TANK.

1%2F%281%2F15-1%2F40%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = the time in minutes to
fill the tank with both pipes open
------------------------------
Add the rate of filling of the filling pipe
and subtract the rate of emptying of
the other pipe
--------------------------------
+1%2F15+-+1%2F40+=+1%2Ft+
Multiply both sides by +120t+
+8t+-+3t+=+120+
+5t+=+120+
+t+=+24+
If both pipes are open, the tank fills in 24 min
-------------------
check:
+1%2F15+-+1%2F40+=+1%2F24+
+.06667+-+.025+=+.041667+
+.04167+=+.041667+
error due to rounding off

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
A tank that hold 400 gallon of water can be filed by one pipe in 15 minutes and emptied by another pipe in 40 minutes.
how mush time does it take to fill tank if both pipes are open?
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