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

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.