Question

Meenakshee cycles to her school at an average speed of $12\mathrm{km}/\mathrm{h}$ and takes $20$minutes to reach her school. If she wants to reach her school in $12$ minutes, her average speed should be

• A. $\frac{20}{3}\mathrm{km}/\mathrm{h}$
• B. $16\mathrm{km}/\mathrm{h}$
• C. $20\mathrm{km}/\mathrm{h}$
• D. $15\mathrm{km}/\mathrm{h}$

Answer 1

The correct option is C

$20\mathrm{km}/\mathrm{h}$

Step 1: Calculate the distance between her school and house.

Given : Average speed of Meenakshi $=12\mathrm{km}/\mathrm{h}$

Know that, $\mathrm{Distance}=\mathrm{Speed}\times \mathrm{time}$

Let the distance between her school and house is $d$,

Understand that $20\mathrm{minutes}$ is equal to the $\frac{20}{60}\mathrm{hours}$. [$1\mathrm{hour}=60\mathrm{minutes}\Rightarrow 1\mathrm{minute}=\frac{1}{60}\mathrm{hours}$]

Therefore,

$\begin{array}{l}d=12\times \frac{20}{60}\\ \Rightarrow d=4 \mathrm{km}\end{array}$

Step 2: Calculate her speed when she want to reach school in $12\mathrm{minutes}$

Understand that $12\mathrm{minutes}$ is equals to$\frac{12}{60}\mathrm{hours}$.

Let her speed is $s\mathrm{km}/\mathrm{h}$.

Therefore,

$$\begin{gathered} s=\frac{4}{12/60}[\mathrm{Speed}=\frac{\mathrm{Distance}}{\mathrm{Time}}] \\ \Rightarrow s=\frac{4\times 60}{12} \\ \Rightarrow s=20\mathrm{km}/\mathrm{h} \end{gathered}$$

Hence the correct answer is option (C).