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Question

Tap A and Tap B can fill up an empty tank in 4 hours.

Tap B and Tap C can fill up the same empty tank in 6 hours.

Tap A and Tap C can fill up the same empty tank in 3 hours.

How many hours will it take to fill up the empty tank if all the taps are turned on at the same time?

(1) 3/4 hours

(2) 3/8 hours

(3) 2 2/3 hours

(4) 6 1/2 hours

 

 

Source: Raffles Girls’ Primary

Answer

Let’s convert to rate of filling up the tank.. It is like  Distance, Speed and Time. 

Distance is 1 tank. Speed is rate of filling up.

Rate of filling up

A + B = 1/4   tank/hr

B + C = 1/6    tank/hr

A + C = 1/3    tank/hr

 

Total rate = ((A+B) + (B+C)+(A+C))/2 = A+B+C

A+B+C = (1/4 + 1/6 + 1/3) /2 =  3/8   tank/hr

Time taken = Distance /speed =  1 tank/(3/8) = 8/3 hrs = 2  2/3 hrs ###

0 Replies 2 Likes ✔Accepted Answer