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.

Let "x" be the time it takes John to build a car. And let "x+15" be the time it takes Brian to build a car.  We know Brian and John takes 4 hours to build a car together.  So let's rewrite everything in rates.

John can do 1/x of a car per hour
Brian can do 1/(x+15) of a car per hour
John plus Brian can do 1/4 of a car per hour.

So we have an equation:  1/x + 1/(x+15) = 1/4

Multiply both sides by 4x(x+15) to remove the fractions.
We get 8x + 60 = x^2 + 15x
This simplifies to:  0 = x^2 + 7x - 60
Factor this to:  0 = (x+12)(x-5)
And we have our two solutions x = -12, 5
Only x = 5 makes sense in our problem.

So it takes John 5 hours to build a car on his own, but it would take Brian 20 hours to build a car on his own. Poor Brian.