It takes Brian 15 hours longer to build a model car than it takes John. If they work together, they can build the model car in 4 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Brian to build the car on his own.

When they work together, it takes John 1/x hours and it takes Brian 1 / (x+15) hours to complete 1/4 of the model.

1/x + 1 / (x+15) = 1/4 / · x (x+15)

x+15 + x = x (x+15) / 4 / · 4

8 x + 60 = x² + 15 x

x² + 15 x - 8 x - 60 = 0

x² + 7 x - 60 = 0

x² + 12 x - 5 x - 60 = 0

x · (x + 12) - 5 · (x + 12) = 0

(x + 12) · (x - 5) = 0

x = - 12 (not accepted) or x = 5

The time taken by Brian: 5 + 15 = 20 hours