A group of college students volunteer to help homeless people during spring break. They are putting the finishing touches on a house they have 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 determine how long it will take them working together to paint the room. How many hours will it take to paint the room?
If Nita can do the piece in 3 hours then in 1 hour she will do 1/3 of the piece; similarly, in 1 hour, 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 these two fractions, we change them both to the common denominator of 12, so it 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 flip the fraction and multiply, so we have 1 * 12/7 = 12/7 = 1.71428….hours, i.e. Answer (1). In their options they didn’t say what x should represent, so I guess it’s the square footage of the room.
respond. If x is the time needed, then 1) is the answer.
explanation:
x=1/(1/3+1/4)=>
x/3+x/4=1.