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:
[tex]\text{Part of room decorated by all in 1 hour}=\frac{1}{4}+\frac{1}{4}+\frac{1}{3}[/tex]
Let us have a common denominator.
[tex]\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}[/tex]
[tex]\text{Part of room decorated by all in 1 hour}=\frac{3}{12}+\frac{3}{12}+\frac{4}{12}[/tex]
[tex]\text{Part of room decorated by all in 1 hour}=\frac{3+3+4}{12}[/tex]
[tex]\text{Part of room decorated by all in 1 hour}=\frac{10}{12}[/tex]
Since together they can decorate 10/12 of the room in 1 hour, so:
[tex]\text{Total time to decorate the room}=\frac{12}{10}\text{ hours}[/tex]
[tex]\text{Total time to decorate the room}=1.2\text{ hours}[/tex]
Let us convert 0.2 hours into minutes.
[tex]0.2\text{ hours}=0.2\text{ hours}\times \frac{60\text{ minutes}}{\text{ hour}}}[/tex]
[tex]0.2\text{ hours}=0.2\times 60\text{ minutes}[/tex]
[tex]0.2\text{ hours}=12\text{ minutes}[/tex]
Therefore, it will take them 1 hour and 12 minutes to decorate the room.
