Three pipes A, B and C can fill a tank in 6 hours. After working at i

Combined rate of work
1/a+1/b+1/c=1/6
Work done by 3 in 2 hrs=2x1/6=1/3
Work left to be done
1-1/3=2/3.
This work is done by b&c in 7 hrs.
Thus Rate of work is
Work/time=2/3/7=2/21
Therefore
1/a-2/21=1/6. Solve the equation a=14 hrs

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i solved this way...
total work to be done = 6 parts.
all together can do 1 part in 1 hour.
2 hours passed - 2 parts were done. so left 4 parts to finish.
4 parts out of total 6 parts is 2/3.
now..A and B finish filling 2/3 in 7 hours. 2/3 divide by 7 = 2/21. this is the rate for A and B.
to find the rate for C, subtract from 1/6 (rate of all three pipes) the rate of A and B (2/21)
1/6 - 2/21 (multiply first fraction by 7, second by 2) = 7/42 - 4/42 = 3/42
now 3/42 is the rate of C. it can fill 3 pools in 42 hours, or one in 14 hours.
answer is C.

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

A, B and C fill the tank in 6 hrs so their combined rate is 1/6 tank/hr
In 2 hrs, they will fill 1/3rd of the tank.

Now leftover 2/3rd of the tank is filled by A and B in 7 hrs. So combined rate of A and B = (2/3)/7 = 2/21 tank/hr

Rates are additive so,
Rate of C = Rate of A,B and C - Rate of A and B = 1/6 - 2/21 = 3/42 = 1/14
Hence, C alone will fill 1 tank in 14 hrs.

Answer (C)

I) Combined, equal time: 6(A+B+R)
II) Combined, unequal time: 9A+9B+2R

Sine both I) & II) do the same work: 6(A+B+R)=9A+9B+2R –> R=3/4(A+B) = the rate we are looking for is 3/4 of the rate of A & B combined

since total rate is 1/6=x+3/4*x –> 3/4*x = 1/14 –> t=14

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