2. There are two pipes A and B connected to a tank of 500 litres capacity. A fills the tank at the rate of 'x' litres/hour, while B drains the tank at 8 litres/hour. If the total time taken by both the pipes to fill the tank is 80 hours, then find the value of x.

A

Let the rate at which pipe A fills the tank be \( x \) litres/hour. Since pipe B drains the tank at 8 litres/hour, the effective rate at which the tank is being filled is:

\[
\text{Net rate} = x - 8 \, \text{litres/hour}.
\]

Given that the tank has a capacity of 500 litres and it takes 80 hours to fill the tank, we can write the equation:

\[
\text{(Net rate)} \times \text{(Time)} = \text{Total capacity}.
\]

Substituting the known values:

\[
(x - 8) \times 80 = 500.
\]

Simplifying the equation:

\[
80x - 640 = 500.
\]

Now, solve for \( x \):

\[
80x = 500 + 640,
\]
\[
80x = 1140,
\]
\[
x = \frac{1140}{80} = 14.25.
\]

So, the value of \( x \) is 14.25 litres/hour.

Would you like more details on this solution?

Here are 5 related questions:
1. What happens if the draining rate of pipe B increases?
2. How would the total time change if the capacity of the tank doubled?
3. What is the total amount of water drained by pipe B in 80 hours?
4. What would be the equation if the draining rate of pipe B were unknown?
5. How would the solution change if pipe B was closed halfway through?

**Tip:** Always ensure units are consistent when solving rate problems involving time and volume.

There are two pipes A and B connected to a tank of 500 litres capacity. A fills the tank at the rate of 'x' litres/hour, while B drains the tank at 8 litres/hour. If the total time taken by both the pipes to fill the tank is 80 hours, then find the value of x.

This detailed solution covers a problem where two pipes, A and B, are connected to a 500-litre tank. Pipe A fills at an unknown rate 'x' litres/hour while Pipe B drains at 8 litres/hour. Learn how to solve for the filling rate using algebraic techniques in this step-by-step guide. Suitable for Grades 8-10.

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