Question

A person goes a distance of 30km on his bicycle. The number of hours taken by him is one less than his average speed in km/h. Find the time taken by him to complete the journey.

Answer 1

Step 1:

Find quadratic equation:

Let us consider that average speed is $xkm/h.$

Since, the number of hours taken by him is one less than his average speed in km/h.

$\therefore \mathrm{Time}=(x-1)\mathrm{hours}.$

Therefore,

$$\begin{gathered} \mathrm{Distance}=\mathrm{Average}\mathrm{speed}\times \mathrm{time} \\ \Rightarrow 30=x\times (x-1) \\ \Rightarrow 30=x^2-x \end{gathered}$$

Step 2:

Calculate time taken by person:

Factorize quadratic equation;

$$\begin{gathered} x^2-x-30=0 \\ \Rightarrow x^2-6x+5x-30=0 \\ \Rightarrow x(x-6)+5(x-6)=0 \\ \Rightarrow (x-6)(x+5)=0 \\ \Rightarrow x-6=0\mathrm{or}x+5=0 \\ \Rightarrow x=6\mathrm{or}x=-5 \end{gathered}$$

Since, the average speed can not be negative.

Therefore, we have to consider $x=6$.

Since, $\mathrm{Time}=x-1$

therefore,

$\mathrm{Time}=6-1=5\mathrm{hours}$

Hence, the time taken by person to complete his journey is 5 hours.