Algebra and Up:
Question: Gerald can paint a fence in 2 hours. Mandy can paint a fence in 3 hours. How long will it take them to paint a fence together?
Answer: 1 hour and 12 minutes
Solution:
Gerald can paint 1 fence in 2 hours, so his rate is 1/2. Mandy can paint 1 fence in 3 hours, so her rate is 1/3. If we let x be the rate at which they can paint a fence together, they can paint 1 fence in x hours, so the rate is 1/x. So our equation is:
1/2 + 1/3 = 1/x
Combine the fractions.
5/6 = 1/x
Find the cross product.
5x = 6
Divide by 5.
x = 6/5 = 1 1/5
Together, Gerald and Mandy can paint a fence in 1 and 1/5 hours, or 1 hour and 12 minutes.
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