Question

Abdul, while driving to school, computes the average speed for his trip to be $20km/hr$. On his return trip along the same route, there is less traffic and the average speed is $30km/hr$. What is the average speed for Abdul's trip?

Answer 1

Step 1: Given Data

Average speed when going, $v_1=20km/hr$

Average speed when returning, $v_2=30km/hr$

Step 2: Determine the time taken when going

Let the total distance be $s$and it will be equal for both the trips.

Let the time taken when going be $t_1$

Therefore, the time taken will be

$$\begin{gathered} t_1=\frac{s}{v_1} \\ =\frac{s}{20} \end{gathered}$$

Step 3: Determine the time taken when returning

Let the time taken when returning be $t_2$

Therefore, the time taken will be

$$\begin{gathered} t_2=\frac{s}{v_2} \\ =\frac{s}{30} \end{gathered}$$

Step 4: Determine the total time taken

The total time taken is,

$$\begin{gathered} t=t_1+t_2 \\ =\frac{s}{20}+\frac{s}{30} \\ =\frac{s}{12} \end{gathered}$$

Step 5: Determine the average speed

The total distance will be $s+s=2s$

Average speed is given by,

$$\begin{gathered} v=\frac{totaldis\tan ce}{totaltime} \\ =\frac{2s}{{\displaystyle \frac{s}{12}}} \\ =24km/hr \end{gathered}$$

Therefore, the average speed for Abdul's trip is $24km/hr$.