Work Problems

Jumat, 17 April 2026

 

Work Problems

 

REVIEW

 

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

Example

 

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.

The equation to solve is  . The LCD is 18t(t + 15).

 

t – 30 = 0       t + 9 = 0   (This does not lead to a solution.)

        t = 30

John needs 30 minutes to paint the wall by himself and Michael needs 30 + 15 = 45 minutes.

 

Practice

 

1.     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?

2.     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?

3.     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?

4.     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?

5.     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?

 

Solutions

 

1.      Let t represent the number of minutes Alex needs to peel the pota- toes. Tina needs t + 5 minutes to complete the job alone.

The equation to solve is . The LCD is 6t(t + 5).

 

t – 10 = 0             t + 3 = 0   (This does not lead to a solution.)

        t = 10

Alex can peel the potatoes in 10 minutes and Tina can peel them in 10 + 5 = 15 minutes.

2.      Let t represent the number of minutes Jared needs to wash the car by himself. The time Rachel needs to wash the car by herself is t + 24.

The equation to solve is . The LCD is 16t(t + 24).

t – 24 = 0             t + 16 = 0   (This does not lead to a solution.)

        t = 24

Jared needs 24 minutes to wash the car alone and Rachel needs 24 + 24 = 48 minutes.

3.    Let t represent the number of hours Printing Press II needs to print the run by itself. Because Printing Press I needs five fewer hours than Printing Press II, t – 5 represents  number of hours Printing Press I needs to complete the run by itself.

The equation to solve is . The LCD is 6t(t – 5).

t – 15 = 0             t – 2 = 0   (This cannot be a solution

        t = 15                            because 2 – 5 is negative.)

Printing Press II can print the run alone in 15 hours and Printing

Press I needs 15 – 5 = 10 hours.

4.      

4.    Let t represent the number of hours Pipe II needs to fill the reservoir alone. Pipe I needs one hour forty minutes less to do the job, so  represents the time Pipe I needs to fill the reservoir by itself.

The equation to solve is . The LCD is 2t(t – ⁵/₃).

(t = ⅔ cannot be a solution because t – ⁵/₃ would be negative)

Pipe II can fill the reservoir in 5 hours and Pipe I can fill it in hours or 3 hours 20 minutes.

5.      Let t represent the number of hours Gary needs to unload the truck by himself. John needs 36 minutes more than Gary needs to unload the truck by himself, so John needs  more hours or ⅗ more hours. The number of hours John needs to unload the truck by himself is ⅗.

Together they can unload the truck in 1 hour 20 minutes, which is hours. This means that the Together rate is ·

The equation to solve is . The LCD is 4t(t – ³/₅).

    

Gary needs 2 ²/₅ hours or 2 hours 24 minutes to unload the truck.

John needs 2 hours 24 minutes + 36 minutes = 3 hours to unload the truck.

 

 

 

“Sumber Informasi”

Labels: Mathematician

Thanks for reading Work Problems. Please share...!