Quadratic Functions, Equations and Inequalities

Quadratic Functions, Equations and Inequalities

Secondary 3

A cyclist travels \(12\) km at a constant speed of \(v\) km/h.
The cyclist returns along the same route at a constant speed of \((v+2)\) km/h. The return journey takes \(30\) minutes less than the outward journey.

  1. Write expressions for the outward and return journey times, in hours.

  2. Form and solve a quadratic equation to find both speeds.

  3. Check that your answers give a difference of \(30\) minutes between the journey times.

Solution:

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Answer:(a) Times \(12/v,\ 12/(v+2)\); (b) \(v^2+2v-48=0\); Speeds \(6,\ 8\text{ km/h}\); (c) Times \(2,\ 1.5\text{ h}\).

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