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## Monday, December 03, 2007

### Ai Tong School P6 CA1 2004 Math Question

Tap A took 3 min to fill up a tank. Tap B took 4 min to fill up the same tank. However, if you pulled out the plug at the bottom of the tank, the tank could be emptied in 12 min. If both the taps are turned on and the plug pulled out at the same time, how long would it take for the tank to be filled up?

Solution

Tap A takes 3 min to fill up tank, while Tap B takes 4 min.

That means that if both taps are turned on at the same time, the ratio of the volume of water in the tank that will be filled by Tap A to the volume of the water in the tank filled by Tap B would be 4:3, because Tap A has a higher rate of water flow.

Volume of Water in Tank filled

Total ----- 7 units

For the tank to be filled by both taps,
Tap A will fill up ----- 4 units divided by 7 units = 4/7 of the tank.

But we know that Tap A takes 3 min to fill up whole tank.

Hence, for Tap A to fill up 4/7 of tank ----- 4/7 x 3 min = 12/7 min.

Therefore, the tank will be full in 12/7 min when both taps are on because 4/7 of the tnak will filled up by Tap A, and the other 3/7 by Tap B.

Rate of water flowing in

12/7 min ----- 1 tank

1/7 min ----- 1/12 tank

1 min ----- 7 x 1/12 tank = 7/12 tank

Rate of water flowing out

12 min ----- 1 tank

1 min ----- 1/12 tank

When both taps are turned on with plug pulled out

Water flowing in – Water flowing out

1 min ---- 7/12 tank – 1/12 tank = 6/12 or 1/2 tank.

Since 1/2 tank takes 1 min to be filled, 1 tank will take 2 min.

Answer: It takes 2 min for tank to be fully filled if both taps are turned on, and with plug pulled out.