Question

Tap A fills a tank in 2 hours, outlet pipes B and C can empty the tank in 4 hours and 6 hours respectively. If the
tank is empty and taps A and B turned on, then how long will it take to fill up? After the tank is full, taps A
and C are all turned on. How long will the tank take to be emptied?

Answer 1

Answer:

Tap A fills a tank in 3 hours

Tap A's 1 hour work = \frac{1}{3}

3

1

Tap B can empty the tank in 4 hours

Tap B's 1 hour work = \frac{1}{4}

4

1

Tap (A+B)'s 1 hour work = \frac{1}{3}-\frac{1}{4}=\frac{1}{12}

3

1

−

4

1

=

12

1

So, the tank will be full in 12 hours

C can empty the tank in 6 hours .

C's 1 hour work = \frac{1}{6}

6

1

Tap (A+B+C)'s 1 hour work = \frac{1}{3}-\frac{1}{4}-\frac{1}{6}=-\frac{1}{12}

3

1

−

4

1

−

6

1

=−

12

1

So, it will take 12 hours to be emptied

Answer 2

Tap A fills a tank in 3 hours

Tap A's 1 hour work =  $\huge{\sf{\frac{1}{3}}$

Tap B can empty the tank in 4 hours

Tap B's 1 hour work =  $\huge{\sf{\frac{1}{4}}$

Tap (A+B)'s 1 hour work =  $\huge{\sf{\frac{1}{3} - \frac{1}{4} = \frac{1}{12}}$

So, the tank will be full in 12 hours

C can empty the tank in 6 hours .

C's 1 hour work =  $\huge{\sf{\frac{1}{6}}$

Tap (A+B+C)'s 1 hour work =  $\huge{\sf{\frac{1}{3}-\frac{1}{4}-\frac{1}{6} = -\frac{1}{12}}$

So, it will take 12 hours to be emptied