Question

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Answer 1

The big man could do 1/3 of a job in 4 hours. The little man could do 1/2 of a job in 2 hours. If the little man needed to complete 30 jobs and worked for 2 hours alone and then was joined by the big man, how long did it take them both to finish the remaining jobs?

Answer 2

Total is 30 jobs, right?

Answer 3

Yes

Answer 4

The rate of the big man is 1/12

Answer 5

Little man does 1/2 job in 2 hours, and he does alone in 2 hours. That means, the leftover is 29.5 jobs, ok?

Answer 6

The rate of the little man is 1/4

Answer 7

Yes.

Answer 8

Their combined rate is 1 job/ 3 hours

Answer 9

So I have to find how long it will take both of them to complete 29.5 jobs with a combined rate of 1/3

Answer 10

Now, for 29.5 jobs.
The Little man work 1/2 job in 2 hours. Hence, to finish 1 job, he has to spend 4 hours, ok?

Answer 11

Understood.

Answer 12

so, in 12 hours, how many jobs has he done?

Answer 13

3 jobs

Answer 14

But the 2 of them combined can do 4 jobs

Answer 15

ok
now for the Big man, he needs 12 hours to finish 1 jobs. Hence in 12 hours, both combine to get 4 jobs done. right?

Answer 16

yes

Answer 17

So, in 84 hours, they get 28jobs done.

Answer 18

That's correct

Answer 19

12 hours /4 jobs
1 jobs/ 3 hours

Answer 20

1.5 jobs/4.5 hours, right?

Answer 21

1.5 jobs in 4.5 hours

Answer 22

Yep

Answer 23

so, combine all, they need 88 hours 30 minutes, right?

Answer 24

That's right, Thank You!

Answer 25

ok