A and B are twos 360 km apart. An express bus departs from A at 8 a.m. and maintains an average speed of 90 km/h between A and B. Another bus starts From B also at 8.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 spots is 60 km/h. Calculate distance distance the two buses at 10 a.m.
In 2 hours without stopping,bus A travels 90*2=180km since bus B stopped for a total of 20 minutes,it is clear it only travelled for 2-1/3=1hour 40mins distance it travelled =5/3*60=100km distance at ten a.m=360-180-100=80km
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To calculate the distance between the two buses at 10 a.m., we need to determine the distance covered by each bus over the 2-hour time period.
Let's first calculate the distance covered by the express bus.
The express bus travels at an average speed of 90 km/h. The time from 8 a.m. to 10 a.m. is 2 hours.
Distance covered by the express bus = Speed × Time
Distance covered by the express bus = 90 km/h × 2 hours
Distance covered by the express bus = 180 km
Now let's calculate the distance covered by the other bus.
The other bus makes four stops at equally spaced points between A and B, with each stop taking 5 minutes. This means that the bus stops for a total of 4 stops × 5 minutes/stop = 20 minutes.
The remaining time for the bus to travel between the stops is 2 hours - 20 minutes = 1 hour and 40 minutes, or 1.67 hours.
The average speed between any two spots is 60 km/h. As there are four equally spaced spots, the distance between each spot is 360 km/4 = 90 km.
Distance covered by the other bus between the stops = Speed × Time
Distance covered by the other bus between the stops = 60 km/h × 1.67 hours
Distance covered by the other bus between the stops = 100.2 km
However, the other bus stops at four different spots, so the total distance covered by the other bus, including the stops, is:
Total distance covered by the other bus = Distance covered between the stops + Distance covered during the stops
Total distance covered by the other bus = 100.2 km + (90 km × 4 stops)
Total distance covered by the other bus = 100.2 km + 360 km
Total distance covered by the other bus = 460.2 km
Therefore, the distance between the two buses at 10 a.m. is the difference between the distances covered by each bus:
Distance between the two buses at 10 a.m. = Distance covered by the express bus - Distance covered by the other bus
Distance between the two buses at 10 a.m. = 180 km - 460.2 km
Distance between the two buses at 10 a.m. = -280.2 km
Since the distance between A and B is 360 km, and the buses are moving in opposite directions, the distance between the two buses at 10 a.m. is 360 km - 280.2 km = 79.8 km.
To calculate the distance between the two buses at 10 a.m., we need to determine the positions of each bus at that time.
Let's start by finding the position of the express bus that departed from A. The express bus maintains an average speed of 90 km/h, so in two hours (from 8 a.m. to 10 a.m.), it would have traveled a distance of 90 km/h × 2 hours = 180 km.
Next, let's find the positions of the other bus that started from B. This bus moves towards A and makes four stops at equally spaced points between B and A. The distance between A and B is 360 km, so each of the four equally spaced points is 360 km / 4 = 90 km apart.
Since this bus moves at an average speed of 60 km/h between any two spots, in two hours it would have traveled a distance of 60 km/h × 2 hours = 120 km between each of the four spots.
From 8 a.m. to 10 a.m., this bus has made two stops. Therefore, it has traveled a distance of 120 km × 2 = 240 km from B towards A.
To determine the positions of the two buses at 10 a.m., we calculate their distances from their respective starting points.
For the express bus, the distance from A is 180 km.
For the other bus, the distance from B is (360 km - 240 km) = 120 km.
Therefore, at 10 a.m., the two buses are 180 km + 120 km = 300 km apart.