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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.

See some of our other supported math practice problems.

### 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.

 1 If 6 workers can harvest a field in 18 hours, how many workers would it have taken to do it in 3 hours? workers 2 If 8 workers can plant a garden in 6 hours, how many workers would it have taken to do it in 4 hours? workers

### 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.

 1 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 2 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

### 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.

 1 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 2 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

### 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.

 1 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 2 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

### 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.

1 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
2 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.

1Peter 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 jobt
+
 1 job16 hours
=
 1 job51/3 hours

2Jennifer 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 job4 hours
+
 1 job6 hours
=
 1 jobt

### 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.

1Mary 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 jobf
+
 1 job2.5f
=
 1 job12.5 hours

Solve for f to get f = 17.5 hours
Working alone, Mary takes f.
2One 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 tankf
-
 1 tank5f
=
 1 tank10 hours

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

### 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.

1One 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 tankf
-
 1 tank5.5f
=
 1 tank16.5 hours

Solve for f to get f = 13.5 hours
Working alone, the slower pipe takes 5.5f.
2One 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 tankf
+
 1 tank2.5f
=
 1 tank7.5 hours

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