SOLUTION: Directions: Tell whether or not the following situation illustrates a quadratic equation. Justify your answer by representing the situation in a mathematical sentence. A motorcy

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Directions: Tell whether or not the following situation illustrates a quadratic equation. Justify your answer by representing the situation in a mathematical sentence. A motorcy      Log On


   

Question 1185757: Directions: Tell whether or not the following situation illustrates a quadratic equation. Justify your answer by representing the situation in a mathematical sentence.
A motorcycle driver travels 15 kph faster than a bicycle rider. The motorcycle driver covers 60 km in two hours less than the time it takes the bicycle to travel the same distance.
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52782) About Me  (Show Source):
You can put this solution on YOUR website!
.

If the question is to find each speed, then the problem can be reduced to this "time" equation


    60%2Fb - 60%2F%28b%2B15%29 = 2 hours.



In the equation, "b" is the speed of the bicycle rider and (b+15) is the speed of the motorcycle driver,

in kilometers per hour.



This equation can be presented as a quadratic equation for unknown variable "b" by multiplying both sides 

of equation (1)  by b*(b+15).


Just answered.




Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
                  SPEEDS          TIMES          DISTANCES

Motorcyclist      r+15          60/(r+15)          60

Bicyclist          r             60/r              60

DIFFERENCE                        2

The time for motorcyclist is less so 60%2Fr-60%2F%28r%2B15%29=2; and this will become a quadratic equation through simplifications.