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

Walter, Bill, and Tom can decorate a room together in 1 hour and 12 minutes by combining their work rates, calculating the total work rate, and then finding the time taken to complete the entire task.

Step-by-step explanation:

Walter, Bill, and Tom are working together to decorate a room. Since it takes Walter and Bill 4 hours each, they can each contribute ¼ of the work per hour. Tom can do the job in 3 hours, contributing ⅓ of the work per hour. To find out how long it will take them all to work together, we add their rates of work.

⅓ (Tom's rate) + ¼ (Walter's rate) + ¼ (Bill's rate) = ¼ + ¼ + ⅓ = ¾ + ⅓.
To find a common denominator, we can use 12, which gives us 3/12 + 3/12 + 4/12 = 10/12. Simplifying that, we get ⅔, meaning they complete ⅔ of the job in one hour together.

To find out how long it will take to complete the entire job, we take 1 (the whole job) and divide it by ⅔ (the part of the job they complete together in one hour). So, 1 divided by ⅔ equals 1.2 hours or 1 hour and 12 minutes. This means that all three working together will take 1 hour and 12 minutes to decorate the room.

Answer 2

Answer: Number of hours they all will take is
`(12)/(7)=1(5)/(7)\ hours`

Step-by-step explanation:

Since we have given that

Number of hours Walter and Bill takes to do the job = 4 hours

Number of hours Tom alone takes to do the job = 3 hours

We need to find the number of hours takes them together to decorate the room.

Work done by Walter and Bill =
`(1)/(4)`

Work done by Tome =
`(1)/(3)`

total work done by three is given by

`(1)/(4)+(1)/(3)\\\\=(3+4)/(12)\\\\=(7)/(12)`

Hence, Number of hours they all will take is
`(12)/(7)=1(5)/(7)\ hours`