anceer wrote:

Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. How many hours will take C alone to fill the tank ?

A. 10

B. 12

C. 14

D. 16

E. 18

1) Combined rate: A, B, and C fill one tank in six hours:

\(\frac{1}{A} +

\frac{1}{B} +

\frac{1}{C} = \frac{1}{6}\)

2) Amt of work finished, work remaining. They work at that rate for 2 hours.

\(r*t = W\)They finish:\((\frac{1}{6}* 2) = \frac{2}{6}= \frac{1}{3}\) tank

Remaining work: \((1 - \frac{1}{3})= \frac{2}{3}\) tank

3) Rate of A and B? C stops. A and B do remaining \(\frac{2}{3}\) in 7 hrs

A and B's combined rate?

\(W/t = r\)\(\frac{(\frac{2}{3})}{7}\) = \(\frac{2}{21}\)

That is, \(\frac{1}{A} +

\frac{1}{B} =

\frac{2}{21}\)

4) Find C's rate. Numbers aren't as bad as they look.

\(\frac{1}{A} +

\frac{1}{B} +

\frac{1}{C} = \frac{1}{6}\)

\(\frac{2}{21} +

\frac{1}{C} = \frac{1}{6}\)

Multiply each term by (6 * 21) = 126

\(12 + \frac{126}{C} = 21\)

\(\frac{126}{C} = 9\)

\(\frac{1}{C} = \frac{9}{126}=\) C's rate

5) C's time?

When work is 1, flip rate to get time. C's time: \(\frac{126}{9}\) = 14 hours

OR

\((\frac{W}{r} = t)\):

\(\frac{1}{(\frac{9}{126})}\)

\(\frac{126}{9}

= 14\) hours

Answer C