Problem of the Week - Algebra and Up - Nov. 15, 2020 to Nov. 21, 2020

Algebra and Up: 

Question: James can paint a fence in 2 hours. Jessie 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:  James can paint 1 fence in 2 hours, so his rate is 1 fence/2 hours. Jessie can paint 1 fence in 3 hours, so her rate is 1 fence/3 hours. If we add their rates together, we get the rate at which they can paint a fence if they work together: 1 fence/2 hours + 1 fence/3 hours = 1 fence/x hours. If we solve for x, we get x = 6/5 = 1 1/5. So, James and Jessie can paint a fence together in 1 1/5 hours, or 1 hour and 12 minutes.