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

Answer:

1.2 hours = 1 hour and 12 minutes.

Step-by-step 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:

$\text{Part of room decorated by all in 1 hour}=\frac{1}{4}+\frac{1}{4}+\frac{1}{3}$

Let us have a common denominator.

$\text{Part of room decorated by all in 1 hour}=\frac{1*3}{4*3}+\frac{1*3}{4*3}+\frac{1*4}{3*4}$

$\text{Part of room decorated by all in 1 hour}=\frac{3}{12}+\frac{3}{12}+\frac{4}{12}$

$\text{Part of room decorated by all in 1 hour}=\frac{3+3+4}{12}$

$\text{Part of room decorated by all in 1 hour}=\frac{10}{12}$

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

$\text{Total time to decorate the room}=\frac{12}{10}\text{ hours}$

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

Let us convert 0.2 hours into minutes.

$0.2\text{ hours}=0.2\text{ hours}\times \frac{60\text{ minutes}}{\text{ hour}}}$

$0.2\text{ hours}=0.2\times 60\text{ minutes}$

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

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

Answer 2

Answer:

1 hour and 12 minutes

Step-by-step explanation:

1. Make A Table

          The Whole Thing   -    In 1 Hour   -  In X Hours

Walter =          4                  =         $\frac{1}{4}$          =         $\frac{x}{4}$

Bill       =          4                  =         $\frac{1}{4}$          =         $\frac{x}{4}$

Tom    =          3                  =          $\frac{1}{3}$         =         $\frac{x}{3}$

2. Make An Equation

$\frac{x}{4}$ + $\frac{x}{4}$ + $\frac{x}{3}$ = 1

$\frac{10x}{12}$ = 1

10x = 12

x = $\frac{12}{10}$ = $\frac{72}{60}$ = 1 12/60 = 1 hour and 12 min

BY THE WAY THIS IS FROM RSM