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Work rate word problems worksheets

Model ten two-worker job stories with reciprocal work rates, exact equations, and worked checks. Every sheet balances five combined-time and five unknown-solo-time problems.

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Read the story, identify the requested quantity and show your reasoning. Include the correct unit in your answer.

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Add exact work rates, then solve

Define x as a completion time. Write each worker reciprocal rate as a fraction of the same one job, then add the exact fractions because both workers start together and work at constant rates without interference.

Each key shows the reciprocal work-rate model first, explains how denominators are cleared, solves the resulting linear equation exactly, and checks that the two job fractions sum to one before rounding.

Learning objective

What this activity builds

Represent each worker as a fraction of one job per hour, solve for the requested time, and verify that the exact work fractions sum to one.

Worked example

Sandy can restock a store in 10 hours and Melanie can do the same job in 6 hours. How long will they take together?

Let x be their time together. x/10 + x/6 = 1, so 16x = 60 and x = 15/4 = 3.75 hours.

Each term is the fraction of the same job completed by one worker. Their exact fractions must add to one whole job.

Teaching notes

Make the practice count

  • Define x and its time role before writing reciprocals.
  • Write the work-rate model before clearing denominators.
  • Keep exact fractions through the check and round only the final answer.

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Math SheetNameScoreTeacherDateWork Word ProblemsDefine x in hours, write the reciprocal work-rate equation first, clear denominators without rounding, solve exactly, and give the final time to the nearest hundredth. Bothworkers start together, complete the same one job, and work at constant additive rates without interference.1. Jessica can reupholster furniture alone in 6 hours. When Dan helps, they start together and complete the same job in 3 hours at constant rates withoutinterference. How many hours would Dan take to complete the job alone?2. Jason can paint a room alone in 8 hours. Mary can complete the same job alone in 4 hours. If they start together and work at constant rates withoutinterference, how many hours will the one job take?3. Alyssa can clean an attic alone in 11 hours. Tim can complete the same job alone in 9 hours. If they start together and work at constant rates withoutinterference, how many hours will the one job take?4. Sally can spread mulch alone in 7 hours. When Mike helps, they start together and complete the same job in 4 hours at constant rates withoutinterference. How many hours would Mike take to complete the job alone?math-sheet.comPage 1 / 3
Math SheetNameScoreTeacherDateWork Word ProblemsDefine x in hours, write the reciprocal work-rate equation first, clear denominators without rounding, solve exactly, and give the final time to the nearest hundredth. Bothworkers start together, complete the same one job, and work at constant additive rates without interference.5. Joan can vacuum a house alone in 11 hours. When Tom helps, they start together and complete the same job in 9 hours at constant rates withoutinterference. How many hours would Tom take to complete the job alone?6. Sam can clean a store alone in 12 hours. Benny can complete the same job alone in 8 hours. If they start together and work at constant rates withoutinterference, how many hours will the one job take?7. Melanie can repair a roof alone in 6 hours. When Benny helps, they start together and complete the same job in 5 hours at constant rates withoutinterference. How many hours would Benny take to complete the job alone?8. Keith can paint a house alone in 12 hours. Sally can complete the same job alone in 10 hours. If they start together and work at constant rates withoutinterference, how many hours will the one job take?math-sheet.comPage 2 / 3
Math SheetNameScoreTeacherDateWork Word ProblemsDefine x in hours, write the reciprocal work-rate equation first, clear denominators without rounding, solve exactly, and give the final time to the nearest hundredth. Bothworkers start together, complete the same one job, and work at constant additive rates without interference.9. Sandy can restock a store alone in 7 hours. Melanie can complete the same job alone in 2 hours. If they start together and work at constant rates withoutinterference, how many hours will the one job take?10. Nancy can trim shrubs alone in 3 hours. When Sara helps, they start together and complete the same job in 2 hours at constant rates withoutinterference. How many hours would Sara take to complete the job alone?math-sheet.comPage 3 / 3

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