Ratio math problem to be solved?

Question

Ugh, How do I solve this?

13. Tim can paint a room in 4 hours that Sara can paint in 3 hours. How long would it

take the two of them working together to paint the room?

A) 1.5hr B) 12/7 hr C) 1/2 hr D) 2 hr E) Answer not given

Answer 1

Tim and Sara are doing one job together.  So...

x/4 + x/3 = 1

1.)  Find a common denominator.

3x/12 + 4x/12 = 12/12

2.)  Add

7x/12 = 12/12

3.) Multiply both sides by 12 (to get rid of the fraction)

7x = 12

4.)  Divide both sides by 7 (to get the x by itself)

x = 12/7

So your answer would be B.

Answer 2

The answer is B, 12/7 hours.

Tim can paint a room in four hours, while Sara can paint on in three. Another way of thinking of this is that Tim can paint 1/4 of a room per hour, and Sara can paint 1/3. If the two work together, every hour they can paint 1/4 + 1/3= 7/12 of the room. So how long will it take them to paint 1 room? You can model the number of rooms the two can paint in x number of hours with the following equation:

Number of rooms = (7/12)x

That is, they can paint 7/12 of a room every hour, so they can paint (7/12)x rooms every x hours. You want to know how many hours it will take them to paint one room, so substitute 1 into Number of rooms.

1= (7/12)x

x= 12/7 hours.  

Answer 3

tim can paint 1/4 a room in an hour and sara can paint 1/3 a room in an hour

1/4 + 1/3 = 7/12 of the room painted in a hour

its going to take 12/7 hours to paint the room