Two different pumps are used to fill an empty water tank. The first pu

should be (D) ?
3T + 2*(T-8) = 72
5T = 88
T = 17.6 h = 17 h 36 min

+1 for option D. The key here is to recognize that if the speed is 2/3 , the time taken becomes 3/2.

If you happen not to see the inverse proportion shortcut, the "long way" is not bad at all. One hitch: at the end add time taken in both stages

Use Stage 1 to find amount of work finished by Pump A working alone. Use Stage 2 to find time for both pumps to finish.

Stage 1: Pump A works alone. Work finished?

Pump A's rate = \(\frac{1}{24}\)
Pump A's time = 8 hours

Work finished by Pump A alone:
\(W=(r*t)=\\
(\frac{1}{24}*8)=\frac{8}{24}=\frac{1}{3}\)
of work is finished
So \(\frac{2}{3}\) remains.

Stage 2: Pumps A and B work together

Pump A's rate =\(\frac{1}{24}\)

Pump B's rate is \(\frac{2}{3}\) of A's rate
Pump B's rate: \((\frac{2}{3}*\frac{1}{24})=\frac{1}{36}\)

Combined rate of A and B:
\((\frac{1}{24}+\frac{1}{36})=(\frac{3}{72}+\frac{2}{72})=\frac{5}{72}\)

Work, W, remaining = \(\frac{2}{3}\)

Time taken by A and B working together?
Time\(=\frac{W}{r}=\frac{\frac{2}{3}}{\frac{5}{72}}=(\frac{2}{3}*\frac{72}{5})=\)
\(\frac{48}{5}\) hours

Total time taken to fill the entire tank?
(Stage 1 + Stage 2) = (8 hrs + \(\frac{48}{5}\) hrs) =
\((\frac{40}{5}+\frac{48}{5})=\frac{88}{5}=17\frac{3}{5}\) hours

ANY fraction of an hour * 60 = # of minutes
(\(\frac{3}{5}\) * 60) = 36 minutes

17 hours, 36 minutes

Answer D

First pump takes 24hrs.
Second pump works at 2/3 the speed of first, hence it takes 3/2 of the time, i.e.36hrs.
Work done per hour by first pump=1/24
Work done per hour by second pump=1/36
Overall work done per hour=1/24+1/36=5/72.
First pump in 8 hrs filled [8*(1/24)] of the tank, i.e. 1/3rd of the tank.
Time taken to fill remaining 2/3 of tank = (2/3)/(5/72) = 9hrs 36min
Therefore overall time taken = 8hrs + 9hrs36min = 17hours 36 min

Let's take the total work as 72 units (LCM of 24 and 36)
A does 72/24 = 3 units of work and B does 72/36 = 2 units of work per hour

For 8 hours A does 8*3 = 24 units of work
Remaining work = 72 -24 = 48 units

A+B together complete 5 units of work

48/5 = 9.xx

Total time: 8+9.xx = 17.xx

Option D