John can paint a room in 3 hours. His apprentice, working alone, requires 6 hours to do the same job.
How long would it take John and his apprentice, working together, to paint the room if they continue to work at the given rates?
John's rate = room/3
Apprent's rate = room/6
combined rate = room/2 + room/6
= 3room/6 = room/2
time at combined rate = room/(room/2))
= 1/(1/2) = 2 hours
To find out how long it would take John and his apprentice to paint the room together, we can use the concept of work rates. The work rate of a person is the amount of work they can complete per unit of time.
Let's assume that the work required to paint the room is one unit of work. Therefore, John's work rate is 1/3 of a room per hour, as he can paint a room in 3 hours. Similarly, the apprentice's work rate is 1/6 of a room per hour.
When they work together, their work rates are added up. So, the combined work rate of John and the apprentice is 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2 of a room per hour.
To find out how long it would take them to paint the whole room working together, we need to invert their work rate. Since their combined work rate is 1/2 of a room per hour, it means they can complete the whole room in 1/(1/2) = 2 hours.
Therefore, working together, John and his apprentice would be able to paint the room in 2 hours.