Question

A tank has 2 taps. If tap A is open, the tank drains empty in 10 min. If tap B is open the tank drains empty in 6 min. How long would it take to drain the tank if both taps are open?

Answer 1

The way to think about these is to realize that one tap is faster, or more efficient, at draining.

Say, for example, tap A drains 60 gallons per minute. The tank drains in 10 minutes, so there are 10 x 60 = 600 gallons. Using tap B, the 600 gallons drains in 6 minutes, so tank B must drain at a rate of 100 gallons per minute.

It turns out that you don't have to know how many gallons are in the tank to get started... that's just an example.

Answer 2

Another possibly easier way to set it up is to say:

t = time to drain using both taps

t x (drain rate of tap A) + t x (drain rate of tap B) = whole tank drained

so, using my earlier example to make the math easy, let's assume there are 600 gallons in the tank:

t (60 gallons per minute) + t (100 gallons per minute) = 600 gallons
t (160) = 600
t = 600/160 = 3.75 minutes.

As I said, it doesn't matter what the tank size is.

Answer 3

t (tank/10 minutes) + t (tank/6 minutes) = tank

all three terms in the above equation have "tank" as a variable, so you can cancel it out, leaving:

t/10 + t/6 = 1

Solve for t...

t will be = 3.75