A car travels up a hill at a constant speed of 19 km/h and returns down the hill at a constant speed of 50 km/h. Calculate the average speed for the round trip.
Am I supposed to add the numbers, divide by two, then subtract two?
This is how the book explains a similar problem: -> 40 + 60 / 2 is 50, then subtract 2 for 48? Is that what's going on?
2 Answers
For this problem (as opposed to the worked example from the book), the answer is $\frac{(2)(50)(19)}{50+19} = \frac{1900}{69} \approx 27.54 km/h$
For equal distances travelled at two constant speeds each, the average speed is the harmonic mean of the two speeds.
Here the $D$ factor in the average speed just cancels out, giving us, $$\text{ average speed } = \frac{2D}{\frac{D}{v_{\text{up}}} + \frac{D}{v_{\text{down}}}} = \frac{2D}{D(v_{\text{up}} + v_{\text{down}})}(v_{\text{up}} v_{\text{down}})= \frac{2(v_{\text{up}} v_{\text{down}})}{v_{\text{up}} + v_{\text{down}}}$$
Substituting the required values, gives us the average speed as $48$ km/hr. Hope it helps.
