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: Let speed of motorbike = $v$ km/h. Car speed = $2v$ km/h.
Step 2: Motorbike starts at 1 pm, car at 2 pm. They meet at 3:40 pm. Motorbike travel time = from 1:00 to 3:40 = 2 hours 40 minutes = $\frac{8}{3}$ hours. Car travel time = from 2:00 to 3:40 = 1 hour 40 minutes = $\frac{5}{3}$ hours.
Step 3: Distance from A to meeting point = $v \times \frac{8}{3} = 168$ km. So $v = 168 \times \frac{3}{8} = 63$ km/h.
Step 4: Car speed = $2v = 126$ km/h. Distance from B to meeting point = $126 \times \frac{5}{3} = 42 \times 5 = 210$ km.
Step 5: Total distance AB = $168 + 210 = 378$ km.
Step 6: Final Answer: 378.