Bob leaves the school walking home at the speed $3$ mph.

At the same time his sister leaves the house and starts biking to school at the speed $12$ mph.

How far from home is their school if they meet in $10$ minutes $?$

Find the distance of the school from home:

Let the distance of the school from their home be $\mathrm{x}$ miles.

The time taken by each of them is:

$\begin{array}{rcl}10\mathrm{minutes}& =& \frac{10}{60}\\ & =& \frac{1}{6}\mathrm{hour}\end{array}$

Speed of Bob walking is $3$ mph and time taken by him is $\frac{1}{6}$ hour .

So, the distance covered by him will be:

$$\begin{gathered} 3\times \frac{1}{6}\left[\mathrm{Distance}=\mathrm{Speed}\times \mathrm{Time}\right] \\ =\frac{1}{2}\mathrm{mile} \end{gathered}$$

Speed of Bob's sister's biking is $12$ mph and time taken by her is $\frac{1}{6}$ hour .

So, the distance covered will be:

$$\begin{gathered} 12\times \frac{1}{6} \\ =2\mathrm{miles} \end{gathered}$$

The distance of home from their school is the sum of distance covered by Bob and his sister:

$\begin{array}{rcl}2+\frac{1}{2}& =& \frac{5}{2}\\ & =& 2.5\\ & & \end{array}$

Hence, the distance of home from their school is $\mathbf{2}\mathbf{.}\mathbf{5}\mathbf{}\mathbf{miles}\mathbf{.}$