Question

Two cities A and B are 360 km apart. A car goes from A to B with a speed of 40 km/hr and returns to A with a speed of 60 km/hr. The average speed of the car is:

• A. 45 km/hr
• B. 48 km/hr
• C. 50 km/hr
• D. 55 km/hr

Hint:

When dealing with average speed over the same distance, use the formula \( \frac{2ab}{a + b} \).

Answer 1

The Correct Option is B

The average speed of a journey to and from two points can be calculated using the formula for average speed: Average Speed = Total Distance / Total Time.
Let's break down the solution step by step:

1. Determine the Total Distance: The car travels from A to B and back to A, which makes the total distance:
   Distance = 360 km (A to B) + 360 km (B to A) = 720 km
2. Calculate the Time for Each Leg of the Journey:
   For the journey from A to B, Speed = 40 km/hr.
   Time taken (A to B) = Distance / Speed = 360 km / 40 km/hr = 9 hours.
   For the journey from B to A, Speed = 60 km/hr.
   Time taken (B to A) = Distance / Speed = 360 km / 60 km/hr = 6 hours.
3. Determine the Total Time:
   Total Time = Time (A to B) + Time (B to A) = 9 hours + 6 hours = 15 hours.
4. Calculate the Average Speed:
   Average Speed = Total Distance / Total Time = 720 km / 15 hours = 48 km/hr.

Therefore, the average speed of the car for the entire journey is 48 km/hr.