Question

Two pipes are used to fill a swimming pool. If the pipe of the larger diameter is used for 4 hours and the pipe of the smaller diameter for 9 hours, only half of the pool can be filled. Find how long it would take for each pipe to fill the pool, separately, if the pipe of smaller diameter takes 10 hours more than the nine of larger diameter to fill the pool.

Answer 1

Let the pipe of larger diameter takes x hours.

∴ The pipe of smaller diameter takes (x + 10) hours to fill the pool.

Now, the part of the pool filled by the larger pipe in 1 hour = `1/x`

The part of the pool filled by the smaller pipe in 1 hour = `1/(x + 10)`

Now, according to question,

`4/x + 9/(x + 10) = 1/2`

`(4(x + 10) + 9x)/(x(x + 10)) = 1/2`

`(4x + 40 + 9x)/(x^2 + 10x) = 1/2`

`(13x + 40)/(x^2 + 10x) = 1/2`

2(13x + 40) = x² + 10x

26x + 80 = x² + 10x

x² + 10x – 26x – 80 = 0

x² – 16x – 80 = 0

x² – 20x + 4x – 80 = 0

x(x – 20) + 4(x – 20) = 0

(x – 20)(x + 4) = 0

x – 20 = 0

x = 20

x + 4 = 0

x = –4,

Not possible as time cannot be negative

∴ Time taken by larger pipe is 20 hours and smaller pipe is x + 10

= 20 + 10

= 30 hours