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, we can use the formula: \[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \] Given: - Average speed from town A to town B = 60 km/h - Average speed from town B to town A = 100 km/h Let's assume the distance between town A and town B is \( d \) km. The time taken to travel from town A to town B is \( \frac{d}{60} \) hours. The time taken to travel from town B to town A is \( \frac{d}{100} \) hours. The total distance traveled is \( 2d \) km (since the car travels from A to B and back to A). The total time taken is \( \frac{d}{60} + \frac{d}{100} \) hours. Now, we can calculate the average speed for the entire journey using the formula: \[ \text{Average Speed} = \frac{2d}{\frac{d}{60} + \frac{d}{100}} \] Let's simplify this expression to find the average speed for the entire journey. Simplify the expression by following steps: - step0: Solution: \(\frac{2d}{\left(\frac{d}{60}+\frac{d}{100}\right)}\) - step1: Remove the parentheses: \(\frac{2d}{\frac{d}{60}+\frac{d}{100}}\) - step2: Add the terms: \(\frac{2d}{\frac{2d}{75}}\) - step3: Multiply by the reciprocal: \(2d\times \frac{75}{2d}\) - step4: Reduce the fraction: \(1\times 75\) - step5: Multiply the terms: \(75\) The average speed for the entire journey is 75 km/h.