A group of college students is volunteering for Homes for the Community during their spring break. They are putting the finishing touches on a house they built. Working alone, Wade can paint a certain room in 4 hours. Rhonda can paint the same room in 3 hours. How long will it take them working together to paint the room? Round your answer to the nearest hundredth if necessary.
0.14 hours
12 hours
1.71 hours
3.5 hours
To solve the problem, we can first find Wade's and Rhonda's individual rates of painting.
Wade can paint the room in 4 hours, so his rate of painting is 1 room per 4 hours, or 1/4 room per hour.
Rhonda can paint the room in 3 hours, so her rate of painting is 1 room per 3 hours, or 1/3 room per hour.
To find their combined rate of painting, we can add their individual rates:
1/4 + 1/3 = (3/12 + 4/12) = 7/12 room per hour.
Now, we can find how long it will take them to paint the room together by dividing the room's size (1 room) by their combined rate of painting:
1 room / (7/12) room per hour = 12/7 hours ≈ 1.71 hours.
Therefore, it will take them approximately 1.71 hours to paint the room together. The answer is 1.71 hours.