Question

Walter, Bill, and Tom want to decorate the multi-purpose room in school for a dance. It would take Walter and Bill 4 hours each to do the job and Tom alone could do the job in 3 hours. If all work together, how long will it take them to decorate the room?

Answer 1

1.2 hours

Explanation:

The time it takes to do a job is given by the formula

1/A + 1/B + 1/C= 1/D

where A is the time it takes person A to do the job

B is the time it takes person B to do the job

C is the time it takes person C to do the job

D is the time it takes A , B,C to do the job together

For this problem A is Walter

B is Bill

C is Tom

D is all the people together

1/4 +1/4+ 1/3 = 1/D

The common denominator is 12 so multiply by 12 on both sides to clear the fraction

12(1/4+1/4 + 1/3 )= 1/D*12

3+3+4 = 12/D

10 = 12/D

Multiply each side by D

10D = 12/D *D

10D =12

Divide by 10

10D/12 = 12/10

D = 1.2 hours

Answer 2

1 hour 12 minutes (1.2 hours)

Explanation:

Since it takes Walter and Bill to finish the job in 4 hours, in 1 hour, they each will do
`(1)/(4)` of the job.

Tom takes 3 hours to do the job, so in 1 hour, he will do
`(1)/(3)` of the job.

Since all of them are working together, they will do
`(1)/(4)+(1)/(4)+(1)/(3)=(5)/(6)` of the job in 1 hour.

So to finish the whole job (1 unit), they will require:

`(1)/((5)/(6))=(6)/(5)` hours

Its going to take them 1.2 hours to finish the job if all of them work together.