A boy rides on his bicycle and goes from his home to school with a uniform speed of 10
km/h and returns back with a speed of 12 km/h. What will be the average speed of the boy?

Solution

Let the distance between the school and the house is x km
Speed of the boy from house to school = 10 km/hr.
Using formula, Time taken = Distance/ speed


So, time taken = x /10 

Also,Speed of the boy from school to the house = 12 km/hr

So, time taken =x/12 hours.
$$\begin{gathered} Average speed =\frac{Total Dis\tan ce}{Total Time} \\ Average speed =\frac{2x}{{\displaystyle \frac{x}{10}}+{\displaystyle \frac{x}{12}}} =\frac{2x}{{\displaystyle \frac{12x +10x}{120}}}=\frac{2x}{{\displaystyle \frac{22x}{120}}} \\ Average speed =\frac{2x}{22 x}\times 120 =10.90 km/hr \end{gathered}$$