Math Problem Statement

  1. 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

Solution

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

Net rate=x8litres/hour.\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:

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

Substituting the known values:

(x8)×80=500.(x - 8) \times 80 = 500.

Simplifying the equation:

80x640=500.80x - 640 = 500.

Now, solve for xx:

80x=500+640,80x = 500 + 640, 80x=1140,80x = 1140, x=114080=14.25.x = \frac{1140}{80} = 14.25.

So, the value of xx 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.

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Math Problem Analysis

Mathematical Concepts

Rate of Work Problems
Linear Equations

Formulas

Net rate of work: (Rate of filling) - (Rate of draining)
Total capacity = (Net rate) × (Time)

Theorems

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Suitable Grade Level

Grades 8-10