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Math Work Problems - Two Persons

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In these lessons, 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.

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: 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

solve the eqn

Answer: The time taken for both of them to mow the lawn together is 24 minutes.


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?
The following video shows another example of algebra work problems.
Igor can do a job in 20 minutes. Fred can do the same job in 30 minutes. How long will the job take if they both work together?

"Working Together" Problems
Word Problem: Work, Rates, Time To Complete a Task. Here 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


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.

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