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.
