# 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.

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

Related Topics: More Algebra Word Problems

Work Problems that involve two persons

Work Problems that involve more than two persons

## Work Problems

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

This formula can be extended for more than two persons.

## “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 Problems with one unknown time

Catherine can paint a house in 15 hours. Dan can paint a house in 30 hours. How long will it take them working together.

Evan can clean a room in 3 hours. If his sister, Faith helps, it takes them two and two-fifths hours. How long will it take Faith working alone?

## Work Problem: Pumps draining a tank

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)

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?

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.