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

To solve this problem  we say that the number of hours it takes John to build the model car is x hours. Therefore the rates of each person to build the car is:

rate of John = 1 car / x hours                                                       ---> 1

rate of Brian = 1 car / (x + 15) hours                                         ---> 2

Since we know that together they can finish the job in 4 hours:

rate of two working together = 1 car / 4 hours                    ---> 3

Now to solve for the value of x, all we have to do is to add equations 1 and 2 and equate this to equation 3:

(1 / x) + (1 / (x + 15)) = 1 / 4

Multiplying everything by 4 (x) (x + 15) to remove the denominators:

4 (x + 15) + 4 x = x (x + 15)

Expanding the equation:

4x + 60 + 4x = x^2 + 15x

x^2 + 7x – 60 =0

Solving for x using the quadratic formula:

x = [-b ± sqrt(b^2 – 4ac)] / 2a

where a = 1, b = 7, c = -60

x = [-7 ± sqrt(7^2 – 4(1)(-60)] / 2(1)

x = -3.5 ± 17

x = -20.5, 13.5

Since time cannot be negative, therefore the answer is:

x = 13.5 hours

time Brian = 13.5 + 15 = 28.5 hours

Therefore it will take Brian 28.5 hours to build a model car.