The distance between Town A and Town B was 210 km. At 9:20 P.M., a bus set off from Town A to Town B and a car left from Town B to Town A. The average speed of the bus was 60 km/h, and the average speed of the car was 80km/h.
a) Calculate the time at which the car passed the bus.
b) How far had the car traveled when it passed the bus?
When they meet, they both would have traveled the same time.
Let that time be t hrs
so 60t + 80t = 210
140t = 210
t = 1.5 hrs
take over
To calculate the time at which the car passed the bus, we need to determine the time it would take for each vehicle to cover the distance between the towns.
a) For the bus:
We are given that the distance between Town A and Town B is 210 km, and the average speed of the bus is 60 km/h. We can use the formula: time = distance / speed.
So, the time taken by the bus to cover the distance is: time = 210 km / 60 km/h = 3.5 hours.
Next, we need to determine at what time the car set off from Town B to Town A. Since both vehicles set off at 9:20 PM, they start their journey at the same time. Therefore, the car also starts at 9:20 PM.
Now that we know the time taken by the bus and the starting time of the car, we can determine the time at which the car passed the bus.
Since the car starts at the same time as the bus, it will take 3.5 hours (the same as the bus) to cover the distance between the towns. So the car would pass the bus after 3.5 hours of traveling.
To calculate the arrival time of the car, we add the travel time of 3.5 hours to the starting time of 9:20 PM.
9:20 PM + 3.5 hours = 12:50 AM
Therefore, the car will pass the bus at 12:50 AM.
b) Now that we know the time at which the car passes the bus, we can determine the distance traveled by the car at that time.
Since we know the time taken by the bus, we can calculate the distance it has traveled when the car passes it. Using the formula: distance = speed × time.
For the bus:
distance = 60 km/h × 3.5 hours = 210 km.
Since the car starts from Town B and passes the bus, it would have traveled the same distance as the bus when passing it. Therefore, the car would have traveled 210 km when it passes the bus.