Question

Walter, Riya, and Teo want to decorate the multi-purpose room in school for a dance. Working alone, Walter and Riya can each do the job in 4 hours while Teo can do the job in 3 hours. If all of them work together, how long will it take them to decorate the room?

Answer 1

To find out how long it will take for Walter, Riya, and Teo to decorate the room together, we need to consider their individual rates of work. Walter and Riya can each do the job in 4 hours, while Teo can do it in 3 hours. By adding up their individual rates, we can determine their combined rate. Taking the reciprocal of this combined rate will give us the time it will take for them to decorate the room together.

Step-by-step explanation:

In order to find out how long it will take for Walter, Riya, and Teo to decorate the room together, we need to consider their individual rates of work. Walter and Riya can each do the job in 4 hours, while Teo can do it in 3 hours.

To find the rate at which they can work together, we can add up their individual rates. Walter and Riya each take 4 hours, so their combined rate is 1/4 + 1/4 = 1/2.

Teo takes 3 hours, so his rate is 1/3.

To find the combined rate when they all work together, we add up the individual rates: 1/2 + 1/3. This is equal to 5/6.

Finally, we can determine how long it will take when they all work together by taking the reciprocal of the combined rate. The reciprocal of 5/6 is 6/5, which is equal to 1 and 1/5 hours. Therefore, it will take them 1 hour and 12 minutes to decorate the room together.