Algebra Work Problems

Work Problems are word problems that involve different people doing work together but at different rates. If the people were working at the same rate then we would use the Inversely Proportional Method instead.

The formula for “Work” Problems that involve two persons is

This formula can be extended for more than two persons. It can also be used in problems that involve pipes filling up a tank.

“Work” Problems: Pipes Filling up a Tank

Example 1:

A tank can be filled by pipe A in 3 hours and by pipe B in 5 hours. When the tank is full, it can be drained by pipe C in 4 hours. if the tank is initially empty and all three pipes are open, how many hours will it take to fill up the tank?

Solution:

Step 1: Assign variables:

Let x = time taken to fill up the tank

Step 2: Use the formula:

Since pipe C drains the water it is subtracted.

Step 3: Solve the equation

The LCM of 3, 4 and 5 is 60

Multiply both sides with 60

Answer: The time taken to fill the tank is hours.

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