Algebra Work Problems
Work Problems that involve two persons
Work Problems that involve more than two persons
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.
In these lessons, we will learn work problems with pipes filling up a tank and work problems with pumps draining a tank.
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 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?
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