Question:A car moves uphill at 40 km/hand then back downhill at 60 km/h. What is the average speed for the round trip?

Speed of the car when moving uphill,s₁ =40 km/h

Speed of the car when moving downhill, s₂=60 km/h

Average speed can be found by dividing the total distance traveled by the total time taken.

The expression for the average speed is as follows:

$s_{avg}=\frac{totaldis\tan ce}{totaltime}$

Let the distance covered uphill be x, and the distance covered downhill be x.

The total time taken for the round trip is calculated as follows:

$∆t=\frac{x}{s_1}+\frac{x}{s_2}$

The total distance covered for the round tripis as follows:

Total distance = x+x =2x

The average speed of the car is calculated as follows:

$$\begin{gathered} S_{avg}=\frac{Totaldis\tan ce}{∆t} \\ =\frac{2x}{{\displaystyle \frac{x}{s_1}}+{\displaystyle \frac{x}{s_2}}} \\ =\frac{2x}{x\left({\displaystyle \frac{s_1+s_2}{s_1{s}_2}}\right)} \\ =\frac{2s_1{s}_2}{s_1+s_2} \end{gathered}$$

Substitute the values in the above expression.

$$\begin{gathered} S_{Avg}=\frac{2\times 40km/h\times 60km/h}{40km/h+60km/h} \\ =48km/h \end{gathered}$$

Therefore, the average speed of the car for the round trip is 48 km/h.