A man is walking at an average speed of 4 miles per hour alongside a railroad track. A freight train, going in the same direction at an average speed of 30 miles per hour, requires 5 seconds to pass the man. How long is the freight train? Give your answer in feet.
What would be the equation?
The answer is 190.67
I wasn't sure if I should re post this.
To solve this problem, we can use the equation Distance = Speed * Time. Let's first convert the speeds from miles per hour to feet per second, as the time given to us is in seconds.
The man is walking at a speed of 4 miles per hour, which is equal to (4 * 5280) feet per hour. To convert this to feet per second, divide by 3600 (since there are 3600 seconds in an hour):
Man's speed = (4 * 5280) ft/hour / 3600 sec/hour = 5.87 ft/sec (approximately)
Similarly, the freight train's speed is 30 miles per hour, which is equal to (30 * 5280) feet per hour. Dividing by 3600 gives us the speed in feet per second:
Freight train's speed = (30 * 5280) ft/hour / 3600 sec/hour = 44 ft/sec (approximately)
Now, let's denote the length of the freight train as 'x'. When the train passes the man, it takes 5 seconds. During this time, both the man and the train would have covered the same distance.
Distance covered by the man = Man's speed * Time = 5.87 ft/sec * 5 sec = 29.35 ft (approximately)
Distance covered by the train = Freight train's speed * Time = 44 ft/sec * 5 sec = 220 ft
Since both distances are the same, we can set up the equation:
Distance covered by the man = Distance covered by the train
29.35 ft = 220 ft
Solving for 'x':
x = 220 ft
Therefore, the length of the freight train is 220 feet.
To find the length of the freight train, we can start by converting the speeds from miles per hour to feet per second. We know that 1 mile is equal to 5280 feet and 1 hour is equal to 3600 seconds.
The man is walking at an average speed of 4 miles per hour, which is equivalent to (4 * 5280) / 3600 = 5.87 feet per second.
The train is traveling at an average speed of 30 miles per hour, which is equivalent to (30 * 5280) / 3600 = 44 feet per second.
Since the train takes 5 seconds to pass the man, we can set up the equation:
Length of train = Relative speed of train with respect to the man * Time taken to pass
Length of train = (44 - 5.87) * 5
Length of train = 190.67 feet
Therefore, the length of the freight train is 190.67 feet.