MATH SOLVE

5 months ago

Q:
# 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?

Accepted Solution

A:

Answer:1 hour 12 minutes (1.2 hours)

Step-by-step explanation:Since it takes Walter and Bill to finish the job in 4 hours, in 1 hour, they each will do [tex]\frac{1}{4}[/tex] of the job.Tom takes 3 hours to do the job, so in 1 hour, he will do [tex]\frac{1}{3}[/tex] of the job.

Since all of them are working together, they will do [tex]\frac{1}{4}+\frac{1}{4}+\frac{1}{3}=\frac{5}{6}[/tex] of the job in 1 hour.

So to finish the whole job (1 unit), they will require:[tex]\frac{1}{\frac{5}{6}}=\frac{6}{5}[/tex] hours

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

Step-by-step explanation:Since it takes Walter and Bill to finish the job in 4 hours, in 1 hour, they each will do [tex]\frac{1}{4}[/tex] of the job.Tom takes 3 hours to do the job, so in 1 hour, he will do [tex]\frac{1}{3}[/tex] of the job.

Since all of them are working together, they will do [tex]\frac{1}{4}+\frac{1}{4}+\frac{1}{3}=\frac{5}{6}[/tex] of the job in 1 hour.

So to finish the whole job (1 unit), they will require:[tex]\frac{1}{\frac{5}{6}}=\frac{6}{5}[/tex] hours

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