Question

two pipes running together can fill a tank in 6 minutes. if one pipe takes 5 minutes more than the other to fill the tank, find the time in which each pipe would fill the tank separately

Answer 1

To find the time each pipe would take to fill the tank separately, we can set up an equation using the concept of work and time. Solving the equation, we find that pipe A would take 10 minutes and pipe B would take 15 minutes.

Step-by-step explanation:

Let's assume that pipe A takes x minutes to fill the tank, and pipe B takes x + 5 minutes to fill the tank.

According to the given information, when both pipes are running together, they can fill the tank in 6 minutes.

Using the concept of work and time, we can set up the following equation:

1/x + 1/(x + 5) = 1/6

To solve this equation, we can multiply both sides by the common denominator: 6x(x + 5).

This simplifies the equation to: 6(x + 5) + 6x = x(x + 5)

Expanding and rearranging the equation, we get: 12x + 30 = x^2 + 5x

Combining like terms, we have: x^2 - 7x - 30 = 0

Factoring the quadratic equation, we find: (x - 10)(x + 3) = 0

So, the possible values for x are 10 and -3. Since time cannot be negative, the time taken by pipe A is 10 minutes and the time taken by pipe B is 15 minutes.