In these lessons, we will learn how to solve work problems that involve two persons who may work at different rates.
Solving Work Word Problems Using Algebra
More Algebra Lessons
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 can use the Inversely Proportional Method instead.
We will learn how to solve math work problems that involve two persons. We will also learn how to solve work problems with unknown time.
The following diagram shows the formula for Work Problems that involve two persons. Scroll down the page for more examples and solutions on solving algebra work problems.
This formula can be extended for more than two persons.
Peter can mow the lawn in 40 minutes and John can mow the lawn in 60 minutes. How long will it take for them to mow the lawn together?
Step 1: Assign variables:
Let x = time to mow lawn together.
Step 2: Use the formula:
Step 3: Solve the equation
The LCM of 40 and 60 is 120
Multiply both sides with 120
Answer: The time taken for both of them to mow the lawn together is 24 minutes.
It takes Andy 40 minutes to do a particular job alone. It takes Brenda 50 minutes to do the same job alone. How long would it take them if they worked together?
We are given that a person can complete a task alone in 32 hours and with another person they can finish the task in 19 hours. We want to know how long it would take the second person working alone.
Latisha and Ricky work for a computer software company. Together they can write a particular computer program in 19 hours. Latisha van write the program by herself in 32 hours. How long will it take Ricky to write the program alone?
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