If two pipes function simultaneously, a reservoir will be filled in 12

1.	If two pipes function simultaneously, a reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours will the second pipe take to fill the reservoir?
Answer» Let the slower pipe fill the reservoir in ‘a’ hours Faster pipe fills it in ‘a – 10’ hours. Given, the two pipes will fill the reservoir together in 12 hours. In 1 hour, part of reservoir filled = 1/12 \(\Rightarrow \frac{1}{a}+\frac{1}{a\,-\,10}=\frac{1}{12}\) ⇒ 12(a + a – 10) = a²– 10a ⇒ 24a – 120 = a²– 10a ⇒ a² - 34a + 120 = 0 ⇒ a² – 30a – 4a + 120 = 0 ⇒ a(a – 30) – 4(a – 30) = 0 ⇒ (a – 4)(a – 30) = 0 Value of a can’t be 4 as (a – 10) will be negative Thus a = 30

If two pipes function simultaneously, a reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours will the second pipe take to fill the reservoir?

Answer»

Let the slower pipe fill the reservoir in ‘a’ hours

Faster pipe fills it in ‘a – 10’ hours.

Given, the two pipes will fill the reservoir together in 12 hours.

In 1 hour, part of reservoir filled = 1/12

\(\Rightarrow \frac{1}{a}+\frac{1}{a\,-\,10}=\frac{1}{12}\)

⇒ 12(a + a – 10) = a²– 10a

⇒ 24a – 120 = a²– 10a

⇒ a² - 34a + 120 = 0

⇒ a² – 30a – 4a + 120 = 0

⇒ a(a – 30) – 4(a – 30) = 0

⇒ (a – 4)(a – 30) = 0

Value of a can’t be 4 as (a – 10) will be negative

Thus a = 30