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2015-06-04T20:28:13+08:00

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We let the rate of the bicycle driver be x, this would make the rate of the motorcycle driver be x+15

So we have the following:
       Rate    Distance      Time
B      x            60            60/x
M     x+15       60           60/(x+15)
* We computed for the time by simply dividing the distance by the rate.

Since the time that the motorcycle driver takes is two hours less than the bicycle to travel 60 km:
60  -     60     = 2
 x       x+15
60x+900-60x = 2
    x(x+15)
900 = 2x²+30x
0 = 2x² + 30x - 900 
0 = x² + 15x - 450 
* This is already the quadratic equation but I will further simplify it

We can perform guess and check by getting the factors of 450 and having an absolute difference of 15:
450 - 1 = 449 X
225 - 2 = 223 X
...
30 - 15 = 15 √

0=(x+30)(x-15) this means the value of x is either -30 or 15.

Or we can factor this out by Quadratic Formula:
x = -15 ± √(15²+1800) = -15 ± √2025 = -15 ± 45 = -30 or 15
                 2                         2                2

So, we cannot have a negative value for x since a rate is never negative.
Therefore the speed of the bicycle driver is 15 kph and the motorcycle driver is 30kph.

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