Math Drills
Work-Rate Problems
3Word Problems
What this worksheet covers
Grade 6 (Elementary School) / Various Word Problems / Work-Rate Problems
The whole is taken as a single 1 and a day's progress is expressed as a fraction. Word problems line up the days when two people or three work at once, cases where one finishes off what another has left, the time for two pipes to fill a tank, and cases reckoned by the product of people and days.
With two working, the job always finishes in fewer days than the faster one alone would take. An answer adding the two counts of days together, or taking the middle of them, crosses that line. Set the answer beside the two counts of days and judge by whether it falls below even the smaller one.
The view of How Savings Grow, which followed an amount piling up, has been replaced here by the form of a percentage with the whole as 1. Crane and Turtle Problems, asking not about progress but about how many of each of two kinds there are, follows after this.
- Two People Working Together1 question
- The Remaining Work1 question
- Three People Working Together1 question
- Water Tank1 question
- Total Person-Days1 question
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Problems and answers on this worksheet
These are the problems in “Various Word Problems”, shown with their answers.
(1)To clean a certain room, person A 1 takes 4 days, and person B 1 takes 12 days. If person A and person B do this job, the 2 of them, in how many days can they finish it? Answer □
Answer: 3days
(2)To finish organizing books, A 1 person working alone would take 15 days. A works first for 5 days, and then B 1 person finishes the rest alone in 4 days. If B 1 person did the whole job alone, how many days would it take? Answer □
Answer: 6days
(3)To organize the books, person A 1 takes 10 days, person B 1 takes 15 days, and person C 1 takes 30 days. If person A, person B, and person C work together on this job, the 3 of them, in how many days can they finish it? Answer □
Answer: 5days
(4)To fill the pool with water, using only Pipe A takes 12 minutes, and using only Pipe B takes 6 minutes. If both pipes are used at the same time, in how many minutes will it be full? Answer □
Answer: 4minutes
(5)Maintaining the schoolyard takes 18 days if 5 people do it. If 9 people do the same job, how many days will it take? Answer □
Answer: 10days
