Question

Abdul while driving to school computes his average speed to be 20 km/hr . on his return trip there is less traffic and his average speed is 30 km/hr . find the average speed of Abdul's trip.

Answer 1

Step 1: Given that:

Average speed of Abdul while driving to school= $20km{h}^{-1}$

Average speed of Abdul while returning from school to home= $30km{h}^{-1}$

Step 2: Calculation of average speed of Abdul's trip:

Average speed= $\frac{Totaldistancecovered}{Totaltimetaken}$

Let, the distance between the school and home of Abdul is $s$ .

If the time taken by Abdul from home to the school is $t_1$ and the time taken in return from school to home is $t_2$ .

Then, using $time=\frac{distance}{speed}$ , we get;

$t_1=\frac{s}{20km{h}^{-1}}$

$t_1==\frac{s}{20}$

And,

$t_2=\frac{s}{30km{h}^{-1}}$

$t_2==\frac{s}{30}$

Now, using the formula for average speed, we have;

$v_{avg}=\frac{s+s}{t_1+t_2}$

$v_{avg}=\frac{2s}{\frac{s}{20}+\frac{s}{30}}$

$v_{avg}=\frac{2s}{\frac{3s+2s}{60}}$

$v_{avg}=\frac{2s\times 60}{5s}$

$v_{avg}=24km{h}^{-1}$

Thus,

The average speed of Abdul in his trip will be $24km{h}^{-1}$ .