Question

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. how long would each pipe take to fill the swimming pool​

Answer 1

Solution:

Let the time taken by the larger pipe be x and time taken by smaller pipe be y.

Therefore,

$\frac{1}{x} + \frac{1}{y} = \frac{1}{24}$

In 1 hour the larger pipe can fill it = 1/x

In 1 hour the smaller pipe can fill it = 1/y

Therefore,

$\frac{8}{x} + \frac{18}{y} = \frac{1}{2}$

$put \: \frac{1}{x} = a \: and \: \frac{1}{y} = b$

a + b = 1/24

24a + 24 = 1

24a + 24 - 1 = 0 ................(1)

$8a + 18b = \frac{1}{2}$

16a + 36b = 1

16a + 36b - 1 = 0 .................(2)

For cross multiplication method, we write the coefficients as

$\frac{a}{ - 24 + 36} = \frac{b}{ - 16 + 24} = \frac{1}{864 - 384}$

$\frac{a}{12} = \frac{b}{8} = \frac{1}{480}$

$\frac{a}{12} = \frac{1}{480} \: and \: \: \frac{b}{8} = \frac{1}{480}$

$a = \frac{12}{480} = \frac{1}{40}$

$b = \frac{8}{480} = \frac{1}{60}$

Hence, x = 40 and y = 60

Therefore,

To fill the full tank the larger pipe takes 40hours.

To fill the full tank the smaller pipe takes 60hours.