The first car covered half of the distance between points A and B at 80 km / h, and the other half at 120 km / h.

The first car covered half of the distance between points A and B at 80 km / h, and the other half at 120 km / h. The second car, moving between points A and B at a constant speed of 100 km / h, spent 6 minutes less than the first. Find the distance between A and B.

1. We take as x (kilometers) the distance between points A and B.
2. The first car covered half of the way in x / 160 hours, the other half in x / 240 hours.
3. We translate minutes into hours:
6 minutes = 6/60 hours = 1/10 hour = 0.1 hour.
4. The second car traveled all the way between points A and B in x / 100 hours.
5. Taking into account that the travel time of the second car is 0.1 hour less than the first one, we make the equation:
x / 160 + x / 240 – x / 10 = 0.1;
x / 16 + x / 24 – x / 10 = 1;
15x + 10x – 24x = 240;
x = 240 kilometers.
Answer: the distance between points A and B is 240 kilometers.