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?
To solve this problem, we first need to determine the speeds of the motorbike and the car. Let's denote the speed of the motorbike as \( v \) km/h. The car's speed is twice that of the motorbike, so its speed will be \( 2v \) km/h.
Step 1: Calculate the total time traveled by each vehicle until they meet.
The motorbike leaves A at 1 pm and meets the car at 3:40 pm. Thus, it travels for a total of 2 hours and 40 minutes, which is \( \frac{8}{3} \) hours.
The car leaves B at 2 pm and meets the motorbike at 3:40 pm, traveling for 1 hour and 40 minutes, which is \( \frac{5}{3} \) hours.
Step 2: Establish the equations for the distance traveled by each vehicle.
The motorbike travels a distance of \( v \times \frac{8}{3} \) km.
The car travels a distance of \( 2v \times \frac{5}{3} \) km.
Since they meet at the point 168 km from A, and since the sum of the distances traveled by both vehicles equals the total distance between A and B, we have:
\[ v \times \frac{8}{3} + 2v \times \frac{5}{3} = \text{Total Distance between A and B} \]