Math Practice Problems - Work Word Problems

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Work Word Problems - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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Complexity=1, Mode=hours

Solve. Simplify all fraction answers and use simple "improper" form. For example, if you get 1 ²/₄, write 3/2.
Decimal form 1.5 is also acceptable.

Complexity=1, Mode=rates

Solve. Simplify all fraction answers and use simple "improper" form. For example, if you get 1 ²/₄, write 3/2.
Decimal form 1.5 is also acceptable.

Complexity=1, Mode=mixed

Solve. Simplify all fraction answers and use simple "improper" form. For example, if you get 1 ²/₄, write 3/2.
Decimal form 1.5 is also acceptable.

Answers

Complexity=1, Mode=man-hours

Solve. Simplify all fraction answers and use simple "improper" form. For example, if you get 1 ²/₄, write 3/2.
Decimal form 1.5 is also acceptable.

Problem

Correct Answer

Your Answer

If 6 workers can harvest a field in 18 hours, how many workers would it have taken to do it in 3 hours?

workers

Solution
Let x be the number of workers it would have taken.

(6 workers)(18 hours)	=	(3 hours)x
108 worker-hours	=	3x hours
36 workers	=	x

Problem

Correct Answer

Your Answer

If 8 workers can plant a garden in 6 hours, how many workers would it have taken to do it in 4 hours?

workers

Solution
Let x be the number of workers it would have taken.

(8 workers)(6 hours)	=	(4 hours)x
48 worker-hours	=	4x hours
12 workers	=	x

Complexity=1, Mode=hours

Solve. Simplify all fraction answers and use simple "improper" form. For example, if you get 1 ²/₄, write 3/2.
Decimal form 1.5 is also acceptable.

Problem

Correct Answer

Your Answer

Peter and Steven take 5¹/₃ hours to do a job. Steven alone takes 16 hours to do the same job. How long would it take Peter to do the same job alone?

hours

Solution
Let t = number of hours for Peter working alone

1 job

16 hours

1 job

5¹/₃ hours

Answer: t = 8 hours

Problem

Correct Answer

Your Answer

Jennifer takes 4 hours to do a job. John takes 6 hours to do the same job. Working together, how many hours will it take them to do the job?

hours

Solution
Let t = number of hours working together

1 job

4 hours

1 job

6 hours

1 job

Answer: t = ¹²/₅ hours

Complexity=1, Mode=rates

Solve. Simplify all fraction answers and use simple "improper" form. For example, if you get 1 ²/₄, write 3/2.
Decimal form 1.5 is also acceptable.

Problem

Correct Answer

Your Answer

Mary works 2.5 times faster than Peter. Together, they do a job in 12.5 hours. How long does it take Mary working alone to do the same job?

hours

Solution
Let f = number of hours it takes Mary working alone
and 2.5f = number of hours it takes Peter working alone

1 job

2.5f

1 job

12.5 hours

Solve for f to get f = 17.5 hours
Working alone, Mary takes f.
Answer: f = 17.5 hours

Problem

Correct Answer

Your Answer

One pipe can empty a tank 5 times faster than another pipe can fill the tank. Starting with a full tank, if both pipes are turned on, it takes 10 hours to empty the tank. How long does it take the slower pipe working alone to fill an empty tank?

hours

Solution
Let f = number of hours it takes the faster pipe and 5f = number of hours it takes the slower pipe

1 tank

10 hours

Solve for f to get f = 8 hours
Working alone, the slower pipe takes 5f.
Answer: 5f = 40 hours

Complexity=1, Mode=mixed

Solve. Simplify all fraction answers and use simple "improper" form. For example, if you get 1 ²/₄, write 3/2.
Decimal form 1.5 is also acceptable.

Problem

Correct Answer

Your Answer

One pipe can empty a tank 5.5 times faster than another pipe can fill the tank. Starting with a full tank, if both pipes are turned on, it takes 16.5 hours to empty the tank. How long does it take the slower pipe working alone to fill an empty tank?

hours

Solution
Let f = number of hours it takes the faster pipe and 5.5f = number of hours it takes the slower pipe

1 tank

5.5f

1 tank

16.5 hours

Solve for f to get f = 13.5 hours
Working alone, the slower pipe takes 5.5f.
Answer: 5.5f = 74.25 hours

Problem

Correct Answer

Your Answer

One pipe can empty a tank 2.5 times faster than another pipe. Starting with a full tank, if both pipes are turned on, it takes 7.5 hours to empty the tank. How long does it take the faster pipe working alone to empty a full tank?

hours

Solution
Let f = number of hours it takes the faster pipe and 2.5f = number of hours it takes the slower pipe

1 tank

2.5f

1 tank

7.5 hours

Solve for f to get f = 10.5 hours
Working alone, the faster pipe takes f.
Answer: f = 10.5 hours

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