I can paint a room in 3 hours. You can paint it in 4 hours. How long will it take if we work together?

Question

I can paint a room in 3 hours. You can paint it in 4 hours. How long will it take if we work together?

Answer 1

It's a work problem. You can set up this way.

 

my rate+your rate=total rate where rate=1 job over hours

 

1/3+1/4=1/x

 

Find "x" and start the problem by multiplying both sides  by the LCD (12x).

 

 

 

Answer 2

Given:

• I can paint a room in 3 hours. You can paint it in 4 hours.

Required:

• How long will it take if we work together?

Solution:

• Let the rate that you can paint the room = 1/3.
• Let the rate that I can paint the room = 1/4.
• Let X equal the unknown, which is how long will it take if we work together

 

• The equation is therefore:

          1/3*X +1/4*X = 1

          Use common denomination of 3*4=12

 

           (4X + 3X)  =  1  This implies that 7X/12 = 1. Solving for X you get X=12/7 = 1.71 hours is the answer.

                 12