Question

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.

Answer 1

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.

took the test but we only had part of this question hope it helps :)

Answer 2

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.