A and B are two towns 360 km apart. An express bus departs from A at B a.m. and maintains an average speed of 90 km/h between A and B. Another bus starts from B also at 8 a,m. and moves towards A making four stops at four equally spaced points between B and A. Each stop is of duration 5 minutes and the average speed between any two stops is 60 km/h. Calculate the distance between the two buses at 10 a.m.
The express bus from A is traveling at a constant speed of 90 km/h, so by 10 a.m. (2 hours later), it would have covered a distance of 180 km.
The other bus from B is making 4 stops at equally spaced points, so each stop is at a distance of (360 km / 4) = 90 km apart. In total, the distance between the two buses is 90 km x 4 = 360 km.
However, we need to account for the time spent at the stops. The bus from B makes 4 stops, each of 5 minutes duration. So in total, it spends 4 x 5 = 20 minutes at stops. Converting this into hours gives us 20 minutes / 60 = 1/3 hours.
In the 2 hours between 8 a.m. and 10 a.m., the bus from B has traveled at an average speed of 60 km/h. Therefore, in 2 hours, it would have traveled 60 km/h x 2 hrs = 120 km.
At 10 a.m., the distance between the two buses would be the total distance between them (360 km) minus the distance that the bus from B has traveled (120 km), minus the distance that the bus from A has traveled (180 km).
Therefore, the distance between the two buses at 10 a.m. is 360 km - 120 km - 180 km = 60 km.
So, the distance between the two buses at 10 a.m. is 60 km.