Rate of Work Problems by D. Fisher Send feedback to fisher_d@madera.k12.ca.us Many images from Wikipedia. by D. Fisher

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Marge can clean the house in 3 hrs. Lisa can clean it in 5 hrs. How long will it take them to clean the house if they both work together?

Marge can clean the house in 3 hrs., Use Unit Rates Marge can clean the house in 3 hrs., so she does 1/3 of the house per hour.

Lisa can clean the house in 5 hrs., Use Unit Rates Lisa can clean the house in 5 hrs., so she does 1/5 of the house per hour.

Let T be the time in hours. 1 1 T + T = 1 3 5

1/3T + 1/5T = 1 15(1/3T + 1/5T) = 15(1) 5T + 3T = 15 8T = 15 T = 15/8 17/8 hrs.

Bart can wash the car in 20 min. Homer can wash it in 30 min. How long will it take them to wash the car if they both work together?

Bart can wash the car in 20 min., so he does 1/20 of the car per min. Use Unit Rates Bart can wash the car in 20 min., so he does 1/20 of the car per min.

Homer can wash the car in 30 min., so he does 1/30 of the car per min. Use Unit Rates Homer can wash the car in 30 min., so he does 1/30 of the car per min.

Let M be the time in minutes. 1 1 M + M = 1 20 30

1/20M + 1/30M = 1 60(1/20M + 1/30M) = 60(1) 3M + 2M = 60 5M = 60 M = 12 min.

Springfield School

Mr. Skinner can enroll 15 students per hr. Mr. Chalmer can enroll 20 students per hr. How long will it take them to enroll 140 students working together?

Minutes work better than hours. Use Unit Rates Minutes work better than hours. Mr. Skinner enrolls 15 students per 60 min., so he enrolls 15/60 or 1/4 students per min.

Minutes work better than hours. Use Unit Rates Minutes work better than hours. Mr. Chalmer enrolls 20 students per 60 min., so he enrolls 20/60 or 1/3 students per min.

1/4M + 1/3M = 140 12(1/4M + 1/3M) = 12(140) 3M + 4M = 1680 7M = 1680 M = 240 min. = 4 hrs.

Grading Papers

Mrs. Krabappel can grade a set of papers in 11/2 hrs. Miss Hoover can grade them in 80 min. How long will it take them to grade one set if they both work together?

Minutes work better than hours. Use Unit Rates Minutes work better than hours. Mrs. Krabappel grades 1/90 of a set per min.

Miss Hoover grades 1/80 of a set per min. Use Unit Rates Miss Hoover grades 1/80 of a set per min.

1/90M + 1/80M = 1 720(1/90M + 1/80M) = 720(1) 8M + 9M = 720 17M = 720 M = 426/17 min.

Approximately how long would it take them to grade 3 sets if they both work together?

1/90M + 1/80M = 3 720(1/90M + 1/80M) = 720(3) 8M + 9M = 2160 17M = 2160 M = 1271/17 min. A little more than 2 hrs.

Math Is Fun