Question

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?

Short answer

Answer

The average speed for the round trip is 48 km/h

Step-by-step solution

Given data

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

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

Understanding the average speed

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:

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

Determination of the average speed

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.