Question

A swimming pool is filled with three taps with uniform flow of water .the first two taps operating simultaneously fill the pool in the same time during which the pool is filled by the third tap alone .find the time required to fill the pool separately

Answer 1

Answer:

same the time

Step-by-step explanation:

because all taps are with the uniform flow

Answer 2

Time taken by tap 1 = 15

Time taken by tap 2 = 10

time taken by tap 3 = 6

Step-by-step explanation:

Let the time taken by tap 1 = x + 5

     the time taken by tap 2 = x

     the time taken by tap 3 = x - 4

Time taken by tap 3 = time take by tap 1 + time take by tap 2

$\frac{1}{x-4} =\frac{1}{x} + \frac{1}{x+5}$

$\frac{1}{x-4} = \frac{x+5+x}{x(x+5)}$

x(x+5) = (x-4) (2x +5)

x² +5x = x(2x +5 ) -4(2x+5)

x² +5x = 2x² + 5x - 8 x -20

x² - 8 x - 20 = 0

x² - 10x + 2x - 20 = 0

x (x-10) + 2( x-10) = 0

(x-10) (x+2) = 0

x = 10, -2

Time cannot be taken as -ve so x = 10

Time taken by tap 1 = 15

Time taken by tap 2 = 10

time taken by tap 3 = 6