S’pore Hokkien Huay Kuan 2007 PSLE Math Prelim Q45

An empty tank was filled with water from two taps. Tap A could fill the tank completely in 2 hours and Tap B could fill it completely in 6 hours. Tap A was turned on first and Tap B was turned on 20 minutes later.

a) What fraction of the tank was filled with water after 20 minutes?
b) How long did it take to fill the rest of the tank completely with water?

Solution

a) (Tap A)
2 hours ----- full tank
1 hour ----- half tank
1/3 hour (20 min) ----- 1/3 x ½ tank = 1/6 tank

Answer: 1/6 of the tank would be filled after 20 min.


b) Tap A takes 2 hours to fill tank completely, while Tap B takes 6 hours.
The ratio of the volume that Tap A to Tap B will fill if both taps are on simultaneously is therefore 6 : 2 or 3 : 1.

Volume filled by
Tap A : Tap B
3 : 1

Since 1/6 has been filled at first, there is another 5/6 to be filled after 20 min.

Out of the 5/6 that has to be filled, Tap A will fill ¾ of it, while Tap B will fill ¼ of it. (Since the ratio of volume that will be filled by Tap A : Tap B is 3:1)

Hence, Tap A -----

Full tank ----- 2 hours
5/6 tank ----- 2 x 5/6 hours = 5/3 hours
¾ of 5/6 tank ----- ¾ x 5/3 hours = 5/4 hours or 75 min.

Answer: It will take 75 min to fill the rest of the tank.

Note – “The Singapore Hokkien Huay Kuan 5-School Combined Prelim Maths” is the common Maths Prelim Exam for Tao Nan, Ai Tong, Chongfu, Nan Chiau and Kong Hwa schools.