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More Algebra Word Problems

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 would use the Inversely Proportional Method instead.
## "Work" Problems: Two Persons

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.

Example:

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?

Solution:

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.

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 with your cousin, you can split a cord of firewood in 5 hours. Working alone, your cousin can complete the job in 7 hours. How long would it take you to split the firewood working alone? (Round up to the nearest minute)

Working Together Problem (Part 1 of 2)
Andy does a job in 2 hours. Billy does the same job in 3 hours. How long does it take to complete this job if they work together?
Working Together Word Problem (Part 2 of 2)
Claire can complete spring-cleaning in a house in 5 hours. Ruth can complete spring-cleaning in the same in 7 hours.
If Claire works for 1 hour alone and then Ruth joins her to finish the cleaning, what is the total time to complete the spring-cleaning?