Math Problem of the Week - Algebra and Up - Feb. 13, 2022 to Feb. 19, 2022

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.