Math Problem Statement
- 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 litres/hour. Since pipe B drains the tank at 8 litres/hour, the effective rate at which the tank is being filled is:
Given that the tank has a capacity of 500 litres and it takes 80 hours to fill the tank, we can write the equation:
Substituting the known values:
Simplifying the equation:
Now, solve for :
So, the value of is 14.25 litres/hour.
Would you like more details on this solution?
Here are 5 related questions:
- What happens if the draining rate of pipe B increases?
- How would the total time change if the capacity of the tank doubled?
- What is the total amount of water drained by pipe B in 80 hours?
- What would be the equation if the draining rate of pipe B were unknown?
- 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