A group of college students is volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Nita can paint a certain room in 3 hours. Jorge can paint the same room in 4 hours. Identify the equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room? 1) x/3 + x/4 =1, 1.71 h 2) 3/x + 4/x =1, 1.75 h 3) 3 + 4 = x; 1.83 h 4) 3/4 + x=1, 3.5 h

### 2 Answers

If Nita can do the room in 3 hrs then in 1 hr she will do 1/3 of the room; similarly , in 1 hr., Jorge will do 1/4 of the room, so if they work together , in 1 hour they will paint 1/3 + 1/4 of the room; to add those two fractions we change them both to the common denominator of 12, so that becomes 4/12 + 3/12 = 7/12. To find out how long to paint the whole room (i.e. 12/12) we divide 1 (i.e. 12/12) by 7/12, and to divide by a fraction you turn the fraction upside upside down and multiply instead, so we get 1 * 12/7 = 12/7 = 1.71428….hours i.e. Answer (1). In their options they haven’t said what x is supposed to represent, so I assume it is the area of the room.

Ans. If x is the time required, then 1) is the answer. explanation: x=1/(1/3+1/4)=>

x/3+x/4=1.