Question

Tara while driving to school computes the average speed for her trip to be 20 km/h. On her return trip along the same route, there is less traffic and the average speed is 40 km/h. What is the average speed for Tara's trip?

• A. 27.7 km/h
• B. 24.7 km/h
• C. 26.7 km/h
• D. 25.7 km/h

Answer 1

The correct option is C

26.7 km/h

Let s be the distance between Tara's home and school.

Let $t_1$ be the time in hours taken for going to school and $t_2$ for returning back home.

So, $t_1$ = $\frac{s}{v_1}$ = $\frac{s}{20}$ h

and $t_2$ = $\frac{s}{v_2}$ = $\frac{s}{40}$ h

Total time taken, T = $t_1$ + $t_2$ = $\frac{s}{20}$ h + $\frac{s}{40}$ h = $\frac{3s}{40}$

Total distance = s + s = 2s

Hence, average speed = $\frac{TotalDistance}{TotalTime}$ = $\frac{2s}{\left(\frac{3s}{40}\right)}$ = 26.7 km/h