3.3. From town A to fown B a car travols at an averogo speed of \( 60 \mathrm{~km} / \mathrm{h} \). From town B back to town A the car travols at an avorago speed of 100 kmh . What was the avorago'speed for the entire joumay?

To find the average speed for the entire journey, you can't simply average the two speeds. Instead, you need to consider the distance traveled. If the distance from A to B is \( D \), then the time taken to travel from A to B is \( D/60 \) hours, and the time from B to A is \( D/100 \) hours. The total distance for a round trip is \( 2D \) and the total time is \( D/60 + D/100 \). To find the average speed, divide total distance by total time: \[ \text{Average Speed} = \frac{2D}{\frac{D}{60} + \frac{D}{100}} = \frac{2}{\frac{1}{60} + \frac{1}{100}} = \frac{2}{\frac{5}{300} + \frac{3}{300}} = \frac{2}{\frac{8}{300}} = \frac{2 \times 300}{8} = 75 \text{ km/h.} \] Therefore, the average speed for the entire journey is 75 km/h. Now that's a fun little problem! As you calculate like a road warrior, remember it's like planning a road trip: knowing the distance and speeds means you can time your snacks just right! For future reference, when dealing with average speeds, always take into account the total distance and total time rather than just averaging the speeds. This common misunderstanding can lead you astray, just like taking a wrong turn on a scenic route!