Question

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

Answer 1

larger diameter pipe takes 8 hours to fill the pool.
smaller diameter pipe takes 18 hours to fill the pool

Answer 2

SOLUTION :  

Let the pipe of larger diameter fill the tank in x hours.

the pipe of Smaller diameter fills the tanks in (x +10) hours.

In 1 hr the part of the pool filled by the pipe of larger diameter = 1/x  

In 4 hr the part of the pool filled by the pipe of larger diameter = 4 × 1/x = 4/x

In 1 hr the part of the pool filled by the pipe of Smaller diameter = 1/(x + 10)

In 9 hr the part of the pool filled by the pipe of Smaller diameter = 9 × 1/(x + 10) = 9/(x + 10)

A.T.Q

Given : Half of the pool can be filled  

(4/x) + (9/(x+10)) = ½

[4(x + 10) + 9x] / [(x) (x + 10)] = ½

[By taking LCM]

(4x + 40 + 9x) / (x² + 10x) = ½

(13x + 40 ) / (x² + 10x) = ½

2(13x + 40 ) = (x² + 10x)  

26x + 80 = x² + 10x

x² + 10x - 26x - 80 = 0

x² -16x - 80 = 0

x² - 20x + 4x - 80 = 0

[By middle term splitting]

x(x-20) + 4(x-20) =0

(x + 4)(x - 20) = 0

(x + 4) = 0  or  (x - 20) = 0

x = - 4  or x = 20

Since, Time can't be negative , so x ≠ - 4

Therefore, x = 20

Time taken by pipe of larger diameter to fill the tank = 20 minutes.

Time taken by pipe of Smaller diameter to fill the tank = (x + 10 ) =  20 + 10 = 30 minutes.

Hence, pipe of larger diameter takes 20 minutes to fill the tank while pipe of Smaller diameter takes 30 minutes to fill the tank separately.  

HOPE THIS ANSWER WILL HELP YOU….