Question

A motorbike leaves point A at 1 pm and moves towards point B at a uniform speed. A car leaves point B at 2 pm and moves towards point A at a uniform speed which is double that of the motorbike. They meet at 3:40 pm at a point which is 168 km away from A. What is the distance, in km, between A and B?

• A. 400
• B. 395
• C. 365
• D. 375
• E. 378

Hint:

Calculate travel times carefully. Use distance = speed × time for each vehicle separately.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
This problem involves relative motion. We calculate speed from the first traveller and use it to find the second traveller's contribution to the total distance.
Step 2: Key Formula or Approach:
Speed = Distance / Time. Total Distance = Distance from A to meeting point + Distance from B to meeting point.
Step 3: Detailed Explanation:
1. Motorbike (from A): Starts at 1 pm, meets at 3:40 pm. Time elapsed = 2 hours 40 minutes = \( 2 \frac{2}{3} = 8/3 \) hours. Distance covered = 168 km. Speed of motorbike (\(v_m\)) = \( 168 / (8/3) = 168 \times 3 / 8 = 21 \times 3 = 63 \) km/h. 2. Car (from B): Starts at 2 pm, meets at 3:40 pm. Time elapsed = 1 hour 40 minutes = \( 1 \frac{2}{3} = 5/3 \) hours. Speed of car (\(v_c\)) = \( 2 \times 63 = 126 \) km/h. Distance covered by car = \( 126 \times (5/3) = 42 \times 5 = 210 \) km. 3. Total Distance AB = Distance by motorbike + Distance by car Total = \( 168 + 210 = 378 \) km.
Step 4: Final Answer:
The distance between A and B is 378 km.