SOLUTION: Two trains 80 metres and 70 metres in length respectively are running in the same direction on parallel tracks. The speed of the first train is 46km/h and that of the second train
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Question 884693: Two trains 80 metres and 70 metres in length respectively are running in the same direction on parallel tracks. The speed of the first train is 46km/h and that of the second train is 36 km/h. In what time will they be completely clear of each other from the moment they meet? Answer by Theo(13342) (Show Source):
the 80 meter train is the fast train at 46 kmph
the 70 meter train is the flow train at 36 kmph
in order for the 80 meter train to completely pass the 70 meter train, it has to travel 150 meters more than the 70 meter train in a certain amount of time.
it starts with the front end of the fast train at the back end of the slow train and it ends with the back end of the fast train at the front end of the slow train.
the fast train is traveling 46 - 36 = 10 kmph faster than the slow train
at this relative rate of speed, the fast train will travel 150 meters farther than the slow train in a certain amount of time which we need to determine.
the formula we will use is rate * time = distance.
since the speed is in kmph, we want the distance to be in km so we divide 150 meters by 1000 to get .15 km.
we plus 10 kmph and .15 km into the formla to get:
10 kmph * time = .150 km
divide both sides of this equation by 10 kmph and we get:
time = .150 km / 10 kmph which then becomes:
time = .015 hours.
since 1 hour is equal to 3600 seconds, then we can convert this equation into seconds by multiplying by 3600 to get:
time = .015 * 3600 seconds which is equal to 54 seconds.
it will take the fast train 54 seconds to travel 150 meters farther than the slow train.
let's see how this works.
the front of the fast train is at the back of the slow train when we start.
in .015 hours, the fast train has traveled 46 * .015 = .69 km while the slow train has traveled 36 * .015 = .54 km.
this means that the front of the fast train is now .69 km further down the track and the back of the slow train is .54 km further down the track.
translate this to meters, this means that the fron of the fast train is now 690 meters further down the track and the back of the slow train is 540 meters further down the track.
we have the front of the fast train at 690 meters and the back of the slow train at 540 meters.
the difference is 150 meters.
this means that the front of the slow train is 540 + 70 = 610 meters further down the track while the back of the fast train is 690 - 80 =610 meters further down the track.
the back of the fast train and the front of the slow train are at the same distance further sown the track which means the fast train has completely passed the slow train.
the data every 10 seconds and the graph of the back of the fast train versus the front of the slow train is shown below:
in this picture:
S = number of seconds.
BOFT = back of fast train
FOFT = front of fast train
BOST = back of slow train
FOST = front of slow train
