A cyclist travels a distance of $15\text{ km}$ at a constant speed of $v\text{ km/h}$. At a cons

Question

A cyclist travels a distance of $15\text{ km}$ at a constant speed of $v\text{ km/h}$. At a constant speed of $(v+3)\text{ km/h}$, the same journey would take $15$ minutes less. Write down expressions, in hours, for the two journey times.[2] Form an equation in $v$ and show that it simplifies to $v^2+3v-180=0$.[2] Find the original speed, and explain why the other root is rejected.[2]

Accepted Answer

(a) $\dfrac{15}{v}\text{ h}$, $\dfrac{15}{v+3}\text{ h}$ (b) $v^2+3v-180=0$ (shown) (c) $12\text{ km/h}$; a speed cannot be negative.

Fractional journey models

Fractional journey models

Solution:

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