A car travels from town A to town B at 40 km/h and returns from B to A at 60 km/h by the same route. What is the average speed of the car for the entire journey?

Introduction / Context:

This is a standard round trip average speed problem where the distances each way are equal but the speeds are different. Many candidates incorrectly choose the simple average of 40 and 60, but the correct average speed must take into account the total time taken for the journey. This question reinforces the formula for average speed in such two way journeys, which is based on the harmonic mean of the speeds.

Given Data / Assumptions:

• Speed from A to B = 40 km/h.
• Speed from B to A = 60 km/h.
• The distance between A and B is the same in both directions.
• Let the one way distance be D kilometres.
• We assume uniform motion at the stated speeds.

Concept / Approach:

Average speed equals total distance divided by total time. If the distances are equal, we can use the harmonic mean formula for speeds v1 and v2: average speed = 2 * v1 * v2 / (v1 + v2). This comes from writing the total time as D / v1 + D / v2 and total distance as 2D. Simplifying 2D divided by that total time yields the harmonic mean. We apply this formula with v1 = 40 and v2 = 60.

Step-by-Step Solution:

Verification / Alternative check:

Assume D = 120 km for easier numbers. Time going at 40 km/h is 120 / 40 = 3 hours. Time returning at 60 km/h is 120 / 60 = 2 hours. Total distance = 240 km and total time = 5 hours. Average speed = 240 / 5 = 48 km/h, which matches our formula based solution. This confirms that 48 km/h is correct.

Why Other Options Are Wrong:

Option 50 km/h is simply a guess and does not arise from any correct calculation. Option 45 km/h is the wrong type of average and is lower than the true value. Option 60 km/h is just one of the given speeds and cannot be the average when part of the journey is at a slower 40 km/h. Only 48 km/h correctly balances the distances and times for the full round trip.

Common Pitfalls:

The main pitfall is using the arithmetic mean (40 + 60)/2 = 50 km/h as the answer. That approach ignores the different times spent at each speed. Another mistake is to miscalculate the combined time when working with fractions, for example adding 1/40 and 1/60 incorrectly. Using an assumed numerical distance such as 120 km often makes the arithmetic clearer and reduces algebraic errors.

Final Answer:

The average speed of the car for the entire journey is 48 km/h.