Find the rate of each ( application of quadratic function )

Question

Two bikers started at the same corner,one going east the other going north.One biker is traveling at 3kph faster than the other,After one hour the two bikers are 15km apart.Find the rate of each

Answer 1

distance = rate*time

 

The distance between the two bikers after 1 hr is the hypotenuse of a right triangle. 

The lengths of the two legs are 1(r) & 1(r+3) where r is the rate of speed of the slower bike.

 

From the Pythagorean theorem:

 

r² + (r+3)² = 15²

r² + r² + 6r + 9 = 225

2r² + 6r - 216 = 0

We can factor out a 2 since all are even numbers

r² + 3r - 108 = 0

 

This can be factored.  The factors of -108 that add to 3 are 12(-9)

 

(r+12)(r-9) = 0

 

r = -12 or r = 9

 

Since the speed will not be negative, the slower bike is moving at 9 kph.

The faster bike is moving at r+3 = 12 kph

Answer 2

Let x = the rate of the biker going north.  The rate of the biker going east is x+3.  distance = rate*time so after one hour they have traveled a distance of x and x+3 respectively.  Draw a right triangle.  One leg is x, the other is x+3.  The hypotenuse is 15 km.  Using the Pythagorean Theorem:

 

x² + (x+3)² = 15²

x² + x² + 6x + 9 = 225

2x² + 6x - 216 = 0

x² + 3x - 108 = 0

 

Solve the quadratic for x.  It does factor.