two trains are traveling toward each other adjacent tracks. one of the trains 230 feet long and is moving at a speed of 60 miles per hour. The other train is 220 feet long and is traveling at the rate of 70 miles per hour. Find the time interval between the moment the trains first meet until they completely pass each other
One way to look at it is to consider one of the trains to be standing still, and the second moving at (60+70) mph or 130 mph.
So from the point when the moving train meets the front of the stationary train to when its end reaches the end of the stationary train is 230+220 ft or 450 ft.
450 ft = 450/5280 miles = .085227.. miles
time = .085227../130
= .000655594 hours
= .03933 minutes
= 2.36 seconds
To find the time interval between the moment the trains first meet until they completely pass each other, we need to determine the time it takes for the trains to cover the total distance between them.
First, let's convert the speeds of the trains from miles per hour to feet per second since the given lengths of the trains are in feet.
The speed of the first train is 60 miles per hour, which is equivalent to (60 * 5280) feet per hour or (60 * 5280) / 3600 feet per second. Simplifying, we get 88 feet per second.
The speed of the second train is 70 miles per hour, which is equivalent to (70 * 5280) feet per hour or (70 * 5280) / 3600 feet per second. Simplifying, we get 102.67 feet per second (rounded to two decimal places).
Now that we have the speeds of the trains in feet per second, we can calculate the time it takes for the trains to meet and pass each other.
Let t be the time interval we want to find.
The distance covered by the first train in time t is 88t (since its speed is 88 feet per second).
The distance covered by the second train in time t is 102.67t (since its speed is 102.67 feet per second).
The total distance covered by both trains is the sum of their lengths: 230 feet + 220 feet = 450 feet.
Therefore, we can set up the equation:
88t + 102.67t = 450
Combining like terms:
190.67t = 450
Dividing both sides by 190.67:
t = 450 / 190.67
Calculating the value:
t ≈ 2.36 seconds (rounded to two decimal places)
So, the time interval between the moment the trains first meet until they completely pass each other is approximately 2.36 seconds.