Question

Two water taps together can fill a tank in 9 3/8 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

9 3/8( in mixed fraction) ​

Answer 1

Answer:

Hope it is helpful for you ......

Answer 2

Given,

Two water taps together can fill a tank in 9 3/8 hours.

The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately.

To find out,

Find the time in which each tap can separately fill the tank.

Solution:

Let the time taken to fill tank by smaller one be 'x'.

Then the water filled in 1 hour is 1/x.

The time taken to fill tank by larger one is 'x-10'.

Then the water filled in 1 hour is 1/x-10.

Time taken by two taps together = 9 3/8 = 75/8

Water filled in 1 hour in tank = 1/75/8 = 8/75

As per the problem,

$\frac{1}{x} + \frac{1}{x - 10} = \frac{8}{75}$

$\frac{x + x - 10}{ x(x - 10)} = \frac{8}{75}$

$75(2x - 10) = 8( {x}^{2} - 10x)$

$150x - 750 = 8 {x}^{2} - 80x$

$8 {x}^{2} - 230x + 750 = 0$

$4 {x}^{2} - 115x + 375 = 0$

Here, a = 4, b = -115, c = 375

By quadratic formula,

$x = \frac{ - b± \: \sqrt{ {b}^{2} - 4ac} }{2a}$

$x = \frac{115± \sqrt{ {115}^{2} - 4(4)(375) } }{2(4)}$

$x = \frac{115± \sqrt{13225 - 6000} }{8}$

$x = \frac{115± \sqrt{7225} }{8}$

$x = \frac{115 + 85}{8} \: and \: x = \frac{115 - 85}{8}$

$x = \frac{200}{8} \: and \: x = \frac{30}{8}$

$x = 25 \: and \: x = 3.75(it \: is \: not \: taken \: as \: the \: value \: of \: x)$

Therefore the time taken by smaller one to fill the tank is 25 hours and by the larger one is x-10 = 25-10 = 15 hours.