Question 1209025: 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.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Answer: 190.667 feet (approximate)
The 6's go on forever but we have to round at some point.
When written as a fraction that length is 572/3.
Explanation
Since we're given the "5 seconds" figure and your teacher wants the answer in feet, let's convert each speed value from mph to feet per second.
These facts will be helpful with the conversion
1 hour = 60*60 = 3600 seconds
5280 feet = 1 mile
To avoid rounding error, I'll use the fractional form whenever I get a decimal result.
In short,
4 mph = (88/15) ft per sec
30 mph = 44 ft per sec.
Let's see how far the man walks in 5 seconds.
distance = rate*time
d = r*t
d = (88/15 ft per sec)*(5 sec)
d = (88*5/15) feet
d = (88/3) feet
d = 29.33333 feet
This result is approximate.
The 3's go on forever.
We'll keep this distance in mind for later.
Specifically I'll use the fraction form of this distance.
Draw two parallel horizontal lines.
Then place points A,B on the lower horizontal line and C,D,E on the upper horizontal line like so
A = the man's starting location
B = where the man ends up after 5 seconds elapse
C = starting location of the caboose
D = starting location of the train's nose
E = point where the caboose ends up after 5 seconds elapse
point D is directly north of point A.
point E is directly north of point B.
Once the caboose reaches point E, the train has effectively passed the man.
L = length of the train = distance from C to D
In order for the entire train to pass the man, the caboose starting at point C must travel the train's length L, plus another extra 88/3 feet that the man has traveled.
It does this in 5 seconds at a rate of 44 ft per second.
distance = rate*time
L+(88/3) feet = (44 ft per sec)*(5 sec)
L+(88/3) = 220
L = 220 - (88/3)
L = 220*(3/3) - (88/3)
L = (660/3) - (88/3)
L = (660-88)/3
L = 572/3
L = 190.667 feet (approximate)
The 6's go on forever but we have to round at some point.
Side notes:
190.6666... ft = 190 ft + (2/3) ft
2/3 of a foot = (2/3)*12 = 8 inches
The train is exactly 190 feet 8 inches.
If you wanted the answer in inches only, then 12*572/3 = 2288 inches is the length of the train.
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