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? and no, its not 1 hour 43 mins.

Answer 1

1 hour and 12 minutes

Explanation:

1. Make A Table

The Whole Thing - In 1 Hour - In X Hours

Walter = 4 =
`(1)/(4)` =
`(x)/(4)`

Bill = 4 =
`(1)/(4)` =
`(x)/(4)`

Tom = 3 =
`(1)/(3)` =
`(x)/(3)`

2. Make An Equation

`(x)/(4)` +
`(x)/(4)` +
`(x)/(3)` = 1

`(10x)/(12)` = 1

10x = 12

x =
`(12)/(10)` =
`(72)/(60)` = 1 12/60 = 1 hour and 12 min

BY THE WAY THIS IS FROM RSM

Answer 2

1.2 hours = 1 hour and 12 minutes.

Explanation:

Walter can decorate the multipurpose room in 4 hours.

The part of room decorated by Walter in 1 hour = 1/4

Bill can decorate the multipurpose room in 4 hours.

The part of room decorated by Bill in 1 hour = 1/4.

Tom can decorate the multipurpose room in 3 hours.

The part of room decorated by Tom in 1 hour = 1/3

When they will work together the part of room decorated in 1 hour by all will be:

`\text{Part of room decorated by all in 1 hour}=(1)/(4)+(1)/(4)+(1)/(3)`

Let us have a common denominator.

`\text{Part of room decorated by all in 1 hour}=(1*3)/(4*3)+(1*3)/(4*3)+(1*4)/(3*4)`

`\text{Part of room decorated by all in 1 hour}=(3)/(12)+(3)/(12)+(4)/(12)`

`\text{Part of room decorated by all in 1 hour}=(3+3+4)/(12)`

`\text{Part of room decorated by all in 1 hour}=(10)/(12)`

Since together they can decorate 10/12 of the room in 1 hour, so:

`\text{Total time to decorate the room}=(12)/(10)\text{ hours}`

`\text{Total time to decorate the room}=1.2\text{ hours}`

Let us convert 0.2 hours into minutes.

`0.2\text{ hours}=0.2\text{ hours}* \frac{60\text{ minutes}}{\text{ hour}}}`

`0.2\text{ hours}=0.2* 60\text{ minutes}`

`0.2\text{ hours}=12\text{ minutes}`

Therefore, it will take them 1 hour and 12 minutes to decorate the room.