Work Problems with Quadratic Equations
Solve work problems by filling in the table below. In the work formula Q = rt ( Q = quantity, r = rate, and t = time), Q is usually “1.” Usually the equation to solve is
Worker 1’s Rate + Worker 2’s Rate = Together Rate.
The information given in the problem is usually the time one or both workers need to complete the job. We want the rates not the times . We can solve for r in Q = rt to get the rates.
Because Q is usually “1,”
The equation to solve is usually
Worker 
Quantity 
Rate 
Time 
Worker 1 
1 
Worker 1’s time 

Worker 2 
1 
Worker 2’s time 

Together 1 
1 
Together time 
Solving Work Problems with Quadratic Equations
Together John and Michael can paint a wall in 18 minutes. Alone John needs 15 minutes longer to paint the wall than Michael needs. How much time does John and Michael each need to paint the wall by himself?
Let t represent the number of minutes Michael needs to paint the wall. Then t + 15 represents the number of minutes John needs to paint the wall.
Worker 
Quantity 
Rate 
Time 
Michael 
1 
t 

John 
1 
t + 15 

Together 
1 
18 
The equation to solve is . The LCD is 18 t ( t + 15).
Michael needs 30 minutes to paint the wall by himself and John needs 30 + 15 = 45 minutes.
Work Problems with Quadratic Equations Practice Problems
Practice
 Alex and Tina working together can peel a bag of potatoes in six minutes. By herself Tina needs five minutes more than Alex to peel the potatoes. How long would each need to peel the potatoes if he or she were to work alone?
 Together Rachel and Jared can wash a car in 16 minutes. Working alone Rachel needs 24 minutes longer than Jared does to wash the car. How long would it take for each Rachel and Jared to wash the car?
 Two printing presses working together can print a magazine order in six hours. Printing Press I can complete the job alone in five fewer hours than Printing Press II. How long would each press need to print the run by itself?
 Together two pipes can fill a small reservoir in two hours. Working alone Pipe I can fill the reservoir in one hour forty minutes less time than Pipe II can. How long would each pipe need to fill the reservoir by itself?
 John and Gary together can unload a truck in 1 hour 20 minutes. Working alone John needs 36 minutes more to unload the truck than Gary needs. How long would each John and Gary need to unload the truck by himself?

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