Question

It takes 12 hours to fill a swimming pool using two pipes. if the pipe of longer diameter is used for 4 hours and the pipe of smaller diameter is used for a hours, only half of the pool is filled. How long would each pipe take to fill the swimming pool?



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Answer 1

Answer:

First pipe will take 20 hours, where as second pipe will take 30 hours.

Answer 2

Answer:

Larger → 20 hours

Smaller → 30 hours

Step-by-step explanation:

Let the pipe with larger diameter and smaller diameter be pipes A and B respectively.  Also, let pipe A work at a rate of x hours/ unit and pipe B work at a rate of Y hours / unit.

According to the question,

x+y=1/12

12x+12y=1 ..........(1)

4x+9y=1/12

8x+18y=1 ............(2)

Multiplying (1) by 2 and (2) by 3

24x+24y=2........(3)

24x+54y=3........(4)

Subtracting equation (4) from (3)

→ -30 = -1

y =1/30

Since 12x + 12y= 1

12x + 12×1/30=1

12x + 2/5 = 1

12x= 1- 2/5

x= 3/5 × 1/12

x = 1/20

Hence, the larger pipe will take 20 hours to fill the pool, whereas the smaller would take 30 hours.