Question

A car travels up a hill at a constant speed of $37km/h$ and returns down the hill at a constant speed of $66km/h$. Calculate the average speed for the whole trip.

• A. $47.4km/h$
  
• B. $58km/h$
  
• C. $96km/h$
  
• D. $12km/h$
  

Answer 1

The correct option is A $47.4km/h$

The average speed is the ratio of total traveled distance to total time taken.

Let $d$ be the total distance traveled by the car.

Thus distance traveled in each journey is $d/2$.

So, the time taken for going up the hill is $t_1=\frac{\left(d/2\right)}{v_1}=\frac{d/2}{37}=\frac{d}{74}$

Time taken for going down the hill is $t_2=\frac{\left(d/2\right)}{66}=\frac{d}{132}$

Thus, average speed is $v_{avg}=\frac{d}{t_1+t_2}=\frac{d}{(d/74+d/132)}=47.4km$