One pipe can fill a tank in (x-2) hours and other pipe can empty the tank in (x+2) hours.If the tank is empty and both the pipes are opened together, the tank is filled in 24 hours.Find how much time will the second pipe take to empty the tank?
Answers
Answer:
The second pipe will take the time to empty the tank is 12 hours.
Step-by-step explanation:
Suppose that volume of the tank is A liters…
First pipe can fill the tank in x–2 hours…
So…
In one hour the Volume filled in by one pipe is…
Volume (In) = A/x–2
Second pipe can fill the tank in x+2 hours…
So…
In one hour the Volume emptied out by second pipe is…
Volume (Out) = A/x+2
If the tank is empty and both the pipes are opened together…
In 1 hour the total volume of the tank will be…
Volume (In) – Volume (Out)
= [(A/x–2)–(A/x+2)]
So, in 24 hours the total volume of the tank will be…
24[(A/x–2)–(A/x+2)]
= 24 × 4/(x² – 4) = 1
= x² – 4 = 96
= x² = 100
∴ x = 10
Filled in time is 10 – 2 = 8 hour.
Emptied out time is 10 + 2 = 12 hour.
Hence time taken by second pipe to empty the tank is...
x+2,
= 10+2 = 12 hrs.
Answer:
12 Hrs
Step-by-step explanation:
One pipe can fill a tank in (x-2) hours and other pipe can empty the tank in (x+2) hours.If the tank is empty and both the pipes are opened together, the tank is filled in 24 hours.Find how much time will the second pipe take to empty the tank?
pipe can fill a tank in (x-2) hours
Tank filled in 1 hr = 1/(x-2)
pipe can empty a tank in (x+2) hours
Tank emptied in 1 hr = 1/(x+2)
Both pipe together can fill tank in 1 hr = 1/(x-2) - 1/(x+2)
= (x+2 -x +2)/(x²-4)
= 4/(x²-4)
tank filled in 24 hrs = 24 × 4/(x²-4) = 96/(x²-4)
96/(x²-4) = 1
=> x²-4 = 96
=> x² = 100
=> x = 10
Second pipe can empty the tank in 10 + 2 = 12 Hrs