SOLUTION: A tank can be filled by one inlet pipe in 15 minutes . it takes an outlet pipe 75 minutes to drain the tank. if the outlet pipe is left open by accident, how long would it take to

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Question 202142: A tank can be filled by one inlet pipe in 15 minutes . it takes an outlet pipe 75 minutes to drain the tank. if the outlet pipe is left open by accident, how long would it take to fill the tank ?
Found 2 solutions by ptaylor, J2R2R:
Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
Let x=amount of time it takes to fill the tank when both pipes are working
Then the tank fills at the rate of 1/x tank per min with both pipes working
The tank fills at the rate of 1/15 tank per min with the inlet pipe
The tank empties at the rate of 1/75 tank per min with the outlet pipe
So, our equation to solve is:
1/15 - 1/75=1/x or
5/75 - 1/75=1/x
4/75=1/x
4x=75
x=18.75 min
CK
(4/75)*18.75=75/75=1 (1 tank, that is)
Hope this helps---ptaylor

Answer by J2R2R(94) (Show Source):
You can put this solution on YOUR website!
If it takes 15 minutes to fill the tank and 75 minutes to empty the tank then the flow in is 5 times as fast as the flow out (=75/15).

Based on the speed of the outflow we have five times as much going in giving an overall filling up rate of four times the emptying rate or four fifths of the filling rate. (5 in minus 1 out = 4 in).

Therefore the time to fill the tank with the filling and emptying happening together will be:

Based on filling speed
5/4 of 15 (because it is going at 4/5 of the rate and will take 5/4 of the time)

Or

Based on emptying speed
1/4 of 75 (because it is going at 4 times the rate and therefore will take 1/4 of the time)

Both give the answer of 75/4 = 18.75 minutes (18 minutes, 45 seconds).