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.
