Question

. Two pipes running together can fill a tank in 11 1

9

minutes. If one pipe

takes 5 minutes more than the other to fill the tank separately, find the

time in which each pipe would fill the tank separately.​

Answer 1

Answer:

First pipe = 20 minutes

Second pipe = 25 minutes

Step-by-step explanation:

Let the time taken by first pipe = x minutes.

And the time taken by second pipe be (x + 5) minutes.

Tank filled by first pipe in 1 minute = 1/x

Tank filled by first pipe in 1 minute = 1/(x + 5)

⇒ 1/x + 1/(x + 5) = 9/100

⇒ (x + 5 + x)/x(x + 5) = 9/100

⇒ (2x + 5)/(x² + 5x) = 9/100

⇒ 200x + 500 = 9x² + 45x

⇒ 9x² + 45x - 200x - 500 = 0

⇒ 9x² - 155x - 500 = 0

⇒ 9x² - 180x + 25x - 500 = 0

⇒ 9x(x - 20) + 25(x - 20) = 0

⇒ (9x + 25) (x - 20) = 0

⇒ x = - 25/9, 20 [It can't be negative]

⇒ x = 20 minutes.

First Pipe = x = 20 minutes

Second Pipe = x + 5 = 20 + 5 = 25 minutes.