Question 1040981: A train 125 m long passes a man , running at 5 km / hr in the same direction in which the train is going, in 10 seconds . The speed of the train is - 45 km/ hr, 50 km/hr ,54km/hr,55km/hr
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate * time = distance.
let r = rate, t = time, d = distance.
formula becomes: r * t = d
for the man, the formula becomes 5*t = d.
this is because the rate of the man is 5 kilometers per hour.
they both start when the front of the train is at the same location as the man.
the train has passed the man when the back of the train is at the same location as the man.
this means that the train must be traveling 125 meters further than the man.
125 meters is equivalent to .125 kilometers.
the formula for the man is 5*t = d
the formula for the train becomes r * t = d + .125
t = 10 seconds which is equal to 10/3600 hours.
the formula for the man becomes 5*10/3600 = d.
you can solve for d to get d = 50/3600 = 5/360 kilometers.
this means that d = 5/360 kilometers which makes d = .01388888... kilometers.
the train has to travel .125 kilometers further than that to completely pass the man.
therefore the formula for the train becomes r * 10/3600 = d + .125.
this makes r * 10/3600 = .01388888... + .125 = .1388888... kilometers.
formula for train becomes r * 10/3600 = .1388888... kilometers.
solve for r to get r = .1388888... * 3600 / 10 = 50 kilometers per hour.
that's your answer.
the man travels at 5 kilometers for 10/3600 hours to make a distance of 50/3600 kilometers.
the train travels at 50 kilometers per hour for 10/3600 hours to make a distance of 500/3600 kilometers.
the difference of 500/3600 and 50/3600 is equal to 450/3600 which is equal to .125 kilometers.
.125 kilometers is equal to 125 meters.
this is the length of the train.
they started when the front of the train was at the same location as the man.
they finished when the back of the train was at the same location as the man.
it was important to get everything in the same measure.
you could work with kilometers per hour and kilometers, or you could work with meters per second and meters.
i chose to work with kilometers per hour and kilometers, so i converted everything to kilometers per hour and kilometers.
125 meters is equal to .125 kilometers.
what makes this problem difficult is the measurements involved.
they're just not simple to work with.
the same problem with simpler measurements would be as follows:
assume the man travels at 5km per hour for a period of 1 hour.
assume the train is 2km long.
they start when the front of the train is at the same location as the man.
in 1 hour, the front of the train must travel 2km longer than the man.
the formula for the man is 5*1 = d which makes d = 5 km.
the front of the train must travel 2km longer in the same time, so the train has to travel 7km in 1 hour.
the formula for the train becomes r*1 = 7 which makes r = 7 km per hour.
the man travels 5 km per hour for 1 hour to travel 5 km.
the front of the train travels 7 km per hour for 1 hour to travel 7 km.
the front of the train has traveled 2km further than the man, therefore the back of the train is at the same location as the man in 1 hour.
the following diagram shows this relationship.
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