A bus left from town A to town B 540km away at 7a.m at an average speed of 60km/hr . Two hours later a car left town A towards at an average speed of 100km/hr . Find the distance and the time from A when the car catches up with the bus
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To find the distance and time when the car catches up with the bus, we can use the concept of relative speed.
Let's assume the time when the car catches up with the bus is "t" hours after the car started. At that time, the bus would have been traveling for (t + 2) hours.
The relative speed of the car with respect to the bus is the difference between their speeds:
Relative speed = Car's speed - Bus's speed
= 100 km/hr - 60 km/hr
= 40 km/hr
Now, to find the time "t" when the car catches up with the bus, we can use the formula:
Distance = Speed * Time
According to the problem, the distance traveled by the car is equal to the distance traveled by the bus when they meet.
Distance traveled by the car = Distance traveled by the bus
Using the formula, we can write the equation:
100t = 60(t + 2)
Simplifying the equation:
100t = 60t + 120
Subtracting 60t from both sides:
40t = 120
Dividing both sides by 40:
t = 3 hours
Therefore, the car catches up with the bus after 3 hours.
To find the distance covered by the car when it catches up with the bus, we can substitute the value of t into the formula:
Distance = Speed * Time
Distance = 100 km/hr * 3 hours
Distance = 300 km
Therefore, the distance from Town A when the car catches up with the bus is 300 km, and the time is 3 hours.
To find the distance and the time from town A when the car catches up with the bus, we need to determine the time it takes for the car to catch up with the bus and then calculate the distance at that time.
First, let's find the amount of time it takes for the car to catch up with the bus. The bus left at 7 a.m and traveled for a certain amount of time before the car caught up, which we'll call 't' hours.
Since the bus travels at an average speed of 60 km/hr, the distance traveled by the bus when the car catches up is 60t km.
The car left town A two hours later at a speed of 100 km/hr. This means that the car traveled for a total of (t - 2) hours to catch up with the bus.
The distance traveled by the car when it catches up is 100(t - 2) km.
Now, since the car catches up with the bus, we can equate the distances traveled by the car and the bus:
60t = 100(t - 2)
Simplifying the equation:
60t = 100t - 200
200 - 60t = 100t
200 = 160t
t = 200/160
t = 1.25 hours
Now that we know the time it took for the car to catch up with the bus is 1.25 hours, we can find the distance from town A at that time.
Distance = Speed × Time
Distance = 100 km/hr × 1.25 hrs
Distance = 125 km
Therefore, when the car catches up with the bus, the distance from town A is 125 km and the time is 1.25 hours.
the speed difference is 40 km/hr
in two hours, the bus has gone 120 km
so, it will take the 2nd bus 120/40 = 3 hours for the car to catch up.
At 12:00 noon both vehicles will have gone 300 km