Question

A tap can fill a tank in 4 hours and a pipe can empty the tank in 6 hours. If both the tap and the pipe are opened together, how long will it take to fill the tank?

Answer 1

Answer:

If we assume a sixty litre tank, then the math is easier.

4 hrs of in flow gives us a full 60L. thus the in-flow rate is 15 L/hr

6 hours of out flow to empty a full 60 L, gives us an out flow rate of 10 L/hr.

Both taps are open, 15 in per hour, 10 out per hour, overall flow rate is plus 5L per hour. 60L divided by 5 equals 12 hours.

It will take 12 hours to fill the tank.

To prove that this works for a tank of any size, takes a bit of algebra.

tank size of X litres. 4 hours to fill means a flow rate of 1/4X L/hr. 6 hours to empty means a flow rate of 1/6X L/hr. to find the difference in the flow and thus the remainder in the tank after any given hour, we subtract the flow rates.

1/4X minus 1/6X is the same as 3/12X minus 2/12X which is 1/12X L/hr. thus to get a full tank of X Litres, would require 12 hours.

hope it helps thank u

Answer 2

★Question:-

A tap can fill a tank in 4 hours and a pipe can empty the tank in 6 hours. If both the tap and the pipe are opened together, how long will it take to fill the tank?

★Answer:-

➳ Time taken by tap A to fill the tank =4hours.

➳ Work done by tap A in 1 hour = $\frac{1}{4}$

➳ Time taken by tap B to empty the full tank =6hours.

➳ Work done by tap B in 1 hour =

$- \frac{1}{6}$

(Since, tap B empties the tank).

➳ Work done by ( A + B ) in 1 hour

➳$\frac{1}{4} - \frac{1}{16}$

➳ $\frac{3 - 2}{12}$

➳ $\frac{1}{2}$ Part of the tank is filled.

Therefore,

The Tap will fill the Tank = 12 hours.

Step-by-step explanation:

Hope my answer helps you alot :)༊

Thank you :)࿐

➳ MizzFabulous❤️࿐