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.
3.5 hours
12 hours
1.71 hours
0.14 hours
To solve this problem, we can use the formula:
1/Time taken by Wade + 1/Time taken by Rhonda = 1/Time taken by both
Let x be the time taken for both of them to paint the room together.
1/4 + 1/3 = 1/x
Multiplying both sides of the equation by 12x (the common denominator):
3x + 4x = 12
7x = 12
x = 12/7
Therefore, it will take them approximately 1.71 hours to paint the room together. So the answer is 1.71 hours, rounded to the nearest hundredth.