Two trains approach each other on parallel tracks. Each has a speed of 20.0 km/hr with respect to the earth. If they are initially 18.0 km apart, how long (in seconds) will it be before they pass each other?
20t + 20t = 18 m.
t = 18/40 = 0.45h = 1620 s.
To determine how long it will take for the two trains to pass each other, we need to first convert their speeds from kilometers per hour to kilometers per second.
Since 1 hour is equal to 3600 seconds, we can calculate the speed in kilometers per second by dividing the speed in kilometers per hour by 3600.
For each train, the speed is 20.0 km/hr. Therefore, the speed in km/s for each train is:
Speed = 20.0 km/hr / 3600 s/hr ≈ 0.00556 km/s
Now we can calculate how long it will take for the two trains to meet. Let's assume that t is the time it takes in seconds.
Distance covered by the first train = Speed × Time = 0.00556 km/s × t
Distance covered by the second train = Speed × Time = 0.00556 km/s × t
Since the trains are moving towards each other, the total distance covered by both trains during t seconds will be equal to the initial distance between them, which is given as 18.0 km.
Thus, the equation becomes:
Distance covered by the first train + Distance covered by the second train = 18.0 km
0.00556 km/s × t + 0.00556 km/s × t = 18.0 km
0.01112 km/s × t = 18.0 km
Dividing both sides of the equation by 0.01112 km/s, we get:
t = 18.0 km / 0.01112 km/s
Simplifying, t ≈ 1617.32 seconds
Therefore, it will take approximately 1617.32 seconds for the two trains to pass each other.