a bus left a petrol station at 9:20am and y traveledat an average speed of 75km/h to a town n at 9:40am a taxi traveled at an average speed of 95m/h left the same petrol station and followedthe route of the bus determine the distance from the petrol station coverd by the taxi at the time it cought up with the bus
Let's start by finding the head start of the bus, i.e., how far it traveled between 9:20am and 9:40am.
Time taken by the bus = 9:40am - 9:20am = 20 minutes = 1/3 hour
Distance traveled by the bus in 1/3 hour = speed x time = 75 x 1/3 = 25 km
So, when the taxi started at 9:40am, the bus was already 25 km ahead of it.
Now, let's find out how long it takes for the taxi to catch up with the bus.
Let t be the time taken by the taxi to catch up with the bus after 9:40am.
Distance traveled by the bus in t hours = distance traveled by the taxi in t hours + 25 km
75t = 95t + 25
20t = 25
t = 5/4 hour
So, the taxi catches up with the bus 5/4 hour after 9:40am, which is at 10:05am.
Now, let's find the distance covered by the taxi by 10:05am.
Distance covered by the taxi in 5/4 hour = 95 x 5/4 = 119 km
Therefore, the distance covered by the taxi from the petrol station when it caught up with the bus was 119 km.