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A car left a city travelling uniformly at a speed of 80 km/h. One and a half hours later, a motorbike starting from the same spot and travelling on the same road, followed the car with a speed of 100 km/h. How much time elapsed after the car left the city before the motorcycle caught up with it?

Question

A car left a city travelling uniformly at a speed of 80 km/h. One and a half hours later, a motorbike starting from the same spot and travelling on the same road, followed the car with a speed of 100 km/h. How much time elapsed after the car left the city before the motorcycle caught up with it?

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Solution

To solve this problem, we need to understand that the motorbike and the car will have travelled the same distance when the motorbike catches up with the car.

  1. First, we calculate the distance the car has travelled before the motorbike starts. The car travels at 80 km/h for 1.5 hours, so it has travelled 80 km/h * 1.5 h = 120 km.

  2. Now, we need to find out how long it takes for the motorbike to travel the same distance. The motorbike travels at a speed of 100 km/h, so it will take 120 km / 100 km/h = 1.2 hours to travel 120 km.

  3. However, we must remember that the motorbike started 1.5 hours after the car. So, the total time elapsed after the car left the city before the motorcycle caught up with it is 1.5 hours (the head start of the car) + 1.2 hours (the time it takes for the motorbike to catch up) = 2.7 hours.

This problem has been solved

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