Two pipes a and b can fill a tank in 36 min. And 45 min. Respectively. A water pipe c can empty the tank in 30 min. First a and b are opened. After 7 min,c is also opened. In how much time, the tank is full?
Answers
Answer:
46 minutes
Step-by-step explanation:
Pipes A and B can fill the tank in 36 minutes and 45 minutes respectively.
Pipes A and B can fill 136 part of the tank and 145 part of the tank respectively in one minute.
Pipes A and B together can fill (136+145)=120 part of the tank in one minute.
Pipe C can empty the tank in 30 minutes.
Pipe C can can empty 130 part of the tank in one minute.
Let the tank be full x minutes after opening pipes A and B.
Pipes A and B operate for x minutes and pipe C operates for x−7 minutes.
Pipes A and B fill x20 part of the tank and pipe C empties x−730 part of the tank during the entire operation, at the end of which the tank is full.
x20−x−730=1⇒3x−2x+1460=1⇒x+1460=1.
x=60−14=46⇒x−7=39.
The tank would be full 46 minutes after opening pipes A and B or 39 minutes after opening pipe C.