Question

It takes 24hours to fill a swimming pool using two pipes.if the pipe of larger diameter is used for 8hours and the pipe of the smaller diameter is used for 18 hours .only half of the pool is filled. How long would each pipe takes to fill the swimming pool

Answer 1

Given:-

It takes 24 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 8 hours and the pipe of the smaller diameter is used for 18 hours. Only half of the pool is filled.

To find :-

How long would each pipe take to fill the swimming pool.

Solution:-

Let A and B be two pipes.

➠So in 1 hour quantity of water filled by pipe A is 1/A and that of pipe B is 1/B. The quantity of water filled by both pipes in one hour is 1/A + 1/B

➠It takes 24 hours by pipes to fill the pool

➠So 1/A + 1/B = 1/24------------(1)

➠The quantity of water filled in 8 hours by pipe A = 8/A

➠The quantity of water filled in 18 hours by pipe B = 18/B

Given that,  half is filled,

➠8/A + 18/B = 1/2-------------(2)

From (1) and (2) we have,

➠x + y = 1/24-------------(3)

➠8 x + 18 y = 1/2----------(4)

Multiply eqn (3) by 8 and eqn (4) by 1

➠8 x + 8 y = 1/3

➠8 x + 18 y = 1/2

Subtracting we get

➠- 10 y = - 1/6

➠y = 1/60

So we have B = 60

The second pipe alone fills in 60 hours

Substituting y = 1/60 in eqn (3) ,

➠x + 1/60 = 1/24

➠120 x = 3  

➠x = 3/120 = 1/40

➠So A = 40 hours

So it will take 40 hours , if the first pipe alone fills the pool.

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