SOLUTION: David can paint a bedroom in 1.5 hr. Jay can paint the same bedroom in 2.75 hr. How long will it take them working together, to paint the room?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: David can paint a bedroom in 1.5 hr. Jay can paint the same bedroom in 2.75 hr. How long will it take them working together, to paint the room?      Log On


   

Question 694593: David can paint a bedroom in 1.5 hr. Jay can paint the same bedroom in 2.75 hr. How long will it take them working together, to paint the room?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
David can paint 1 bedroom in 1.5 hr. Therefore David's painting rate is

%221_bedroom%22%2F%221.5_hr%22%22%22=%22%221%2F1.5bedroom%2Fhr%22%22=%22%221%2F1%261%2F2bedroom%2Fhr%22%22=%22%221%2F%283%2F2%29bedroom%2Fhr%22%22=%22%221%2Aexpr%282%2F3%29bedroom%2Fhr%22%22=%22%222%2F3bedroom%2Fhr

Jay can paint 1 bedroom in 2.75 hr. Therefore Jay's painting rate is

%221_bedroom%22%2F%222.75_hr%22%22%22=%22%221%2F2.75bedroom%2Fhr%22%22=%22%222%263%2F4bedroom%2Fhr%22%22=%22%221%2F%2811%2F4%29bedroom%2Fhr%22%22=%22%221%2Aexpr%284%2F11%29bedroom%2Fhr%22%22=%22%224%2F11bedroom%2Fhr

Suppose that together they can paint 1 bedroom in x hr.  Then their combined
painting rate is

%221_bedroom%22%2F%22x_hr%22%22%22=%22%221%2Fxbedroom%2Fhr

The sum of their painting rates must equal to their combined painting rate.
--[Just as in other problems when we find the sum of a boat's rate and the rate of the current]--

          2%2F3bedroom%2Fhr%22%22%2B%22%224%2F11bedroom%2Fhr%22%22=%22%221%2Fxbedroom%2Fhr

                  2%2F3%22%22%2B%22%224%2F11%22%22=%22%221%2Fx

Solve that by multiplying through by the LCD of 33x and you get x = 33%2F34hr 
or about 0.97 hr or about 58 minutes.

Edwin