# Algebra Work Problems

In these lessons, we will learn work problems with pipes filling up a tank and work problems with pumps draining a tank.

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.

The following diagram shows the formula for Work Word Problems. Scroll down the page for more examples and solutions for work word problems. ### “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.

### Work Problem: Pumps draining a tank

Example:
A swimming pool can be emptied in 6 hours using a 10-horsepower pump along with a 6-horsepower pump. The 6-horsepower pump requires 5 hours more than the 10-horsepower pump to empty the pool when working by itself.
How long will it take to empty the pool using just the 10-horsepower pump?

Cooperative Work Word Problems (Time to Finish)

Examples:

1. Pump A can empty a pool in 20 hours and pump B can empty it in 24 hours. Working together, how long will it take to empty the pool?

2. A painter can paint a building in 15 days and a coworker can do the same job in 10 days. If the first painter starts and 3 days later the coworker joins in to help finish the job, how many days doe it take to paint the building?

Rates of Performing Work Problems

Example:
It takes 12 hours to fill a water tank. It takes 16 hours to drain the same water tank. How long will it take to fill the tank if the drain is left open?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 