A can paint a room in 3 hours, and B can paint a room in 4 hours. How long will it take if they paint it together?

Use the equation

Tt = 1/Tf + 1/Ts

where Tt is the total time, Tf is the first person's time, and Ts is the second person's time. Now just plug and chug.

ah:

{ 1/Tt } = 1/Tf + 1/Ts

because
A --> 1/3 rooms per hr
B --> 1/4 rooms/hr
(A+B) --> 1/3 + 1/4 rooms/hr = 7/12 rooms per hr
which is 12/7 hours/room

7/12

To find out how long it will take for A and B to paint the room together, we need to calculate their combined painting rate.

First, let's determine their individual painting rates:

- A can paint a room in 3 hours, so his painting rate is 1/3 of a room per hour.
- B can paint a room in 4 hours, so his painting rate is 1/4 of a room per hour.

To find the combined painting rate, we add their individual painting rates:

1/3 + 1/4 = (4/12) + (3/12) = 7/12

So, A and B together can paint 7/12 of a room per hour.

To find out how long it will take them to paint the whole room together, we divide the total room (which is 1) by their combined painting rate:

1 / (7/12) = 12/7

Therefore, A and B will take approximately 1.71 hours (or 1 hour and 43 minutes) to paint the room together.