Two pipes running together can fill a tank in 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.

Let the faster pipe fill the tank in ‘a’ min.

Given: Slower pipe fills it in ‘a + 5’ min.

To find: Time taken by each pipe.

Method Used:

To solve the quadratic equation by factorisation method, follow the steps:

1) Multiply the coefficient of x² and constant term.

2) factorise the result obtained in step 1.

3) Now choose the pair of factors in such a way that after adding or subtracting(splitting) them

You get coefficient of x.

Explanation:

The faster pipe fills the tank in ‘a’ min.

Slower pipe fills it in ‘a + 5’ min.

Given, the pipes running together can fill a tank in

In 1 min, part of tank filled

The faster pipe fills in 1 min

The slower pipe fills in 1 min

According to the question,

⇒ 100(a + a + 5) = 9(a² + 5a)

⇒ 200a + 500 = 9a² + 45a

⇒ 9a² – 155a - 500 = 0

⇒ 9a² – 180a + 25a - 500 = 0

⇒ 9a (a – 20) + 25(a – 20) = 0

⇒ (9a + 25) (a – 20) = 0

⇒ a = 20 mins

Slower pipe will fill it in a+5 = 25 min