10.7k views
1 vote
Two pipes are connected to the same tank. When working together, they can fill in 2hrs. The larger pipe, working alone, can fill the tank in 3 hrs less time than the smaller one. How long would the smaller one take, working alone, to fill the tank?

User Schanq
by
7.1k points

1 Answer

3 votes

Answer:

The smaller pipe can fill the tank in 6 hours alone.

Explanation:

Let us assume that the smaller pipe can fill the tank alone in x hours and the larger pipe fills it in (x - 3) hours.

Therefore, the smaller pipe in 1 hour can fill
(1)/(x) part of the tank.

Again the larger pipe in 1 hour can fill
(1)/(x - 3) part of the tank.

So, if both the pipes are open then, in 1 hour they can fill (
(1)/(x) + (1)/(x - 3) = (2x - 3)/(x(x - 3)) part of the tank.

Therefore, they can fill the full tank in
(x(x - 3))/(2x - 3) hours.

As per given condition, we can write


(x(x - 3))/(2x - 3) = 2

⇒ x² - 3x = 4x - 6

⇒ x² - 7x + 6 = 0

⇒ (x - 6)(x - 1) = 0

x = 6 or x = 1

But x can not be less than 2 hours.

So, x = 6 hours.

Therefore, the smaller pipe can fill the tank in 6 hours alone. (Answer)

User Amna Ahmed
by
8.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories