Question 154584
An inlet pipe can fill a tank in 1 hour; a drain pipe can empty it in 3/2 hours. The inlet pipe was opened at 6:00 a.m. to fill the tank. At 6:20 a.m. someone noticed that the drain has been left open and so he closes it immediately. How long will it take the first pipe to finish filling.
:
Let's deal in minutes here:
Inlet time = 60 min
Drain time = 90 min
:
let t = time (in minutes) required to finish filling the tank.
:
Let the full tank = 1:
:
Total on time for the inlet pipe = (t+20)
On time for the drain = 20 min
:
{{{((t+20))/60}}} - {{{20/90}}} = 1
Multiply equation by 180 to get rid of the denominators, results:
3(t+20) - 2(20) = 180
:
3t + 60 - 40 = 180
3t + 20 = 180
3t = 180 - 20
3t = 160
t = {{{160/3}}}
t = 53.333 min or 53 min 20 sec to finish filling the tank
:
:
Check with calc (inlet time: 53.33 + 20 = 73.33)
(73.33/60) - (20/90) = 1