Rate of-work

by D. Fisher

Copyright• Notice: All of the images used in this

presentation are from the internet and are publicly available. Many of them came from Wikipedia.

• The content of these presentations are provided by teachers and are presumed to be in the public domain.

• If any of these materials are used inappropriately, please inform the author, and they will be removed immediately or credit given.

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.,

so she does 1/3 of the house per hour.

Lisa can clean the house in 5 hrs.,

so she does 1/5 of the house per hour.

Let T T be the time in hours.

13 TT + 1

5 TT = 1

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.

Homer can wash the car in 30 min.,

so he does 1/30 of the car per min.

Let M M be the time in minutes.

120 MM + 1

30 MM = 1

1/20M + 1/30M = 1

60(1/20M + 1/30M) = 60(1)

3M + 2M = 60

5M = 60

M = 12 min.

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.

Mr. Skinner enrolls 15 students per 60 min.,

so he enrolls 15/60 or 1/4 students per min.

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 = 1680M = 240 min.

= 4 hrs.

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.

Mrs. Krabappel grades 1/90 of a set per min.

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.