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
The formula for “Work” Problems that involve two persons is
This formula can be extended for more than two persons.
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?
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.
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?
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?