Trainspotters Brian A and Brian T stand back-to-back next to a railway line. When the front of a train passes them, Brian A starts walking in the opposite direction of the train, while Brian T walks in the direction of the train.
They walk at exactly the same speed, stopping precisely when the back of the train passes. If Brian A walks exactly 20 metres, and Brian T walks exactly 30 metres, how long is the train?
Answer: 120 metres as smartly worked out (see solutions below) by: France Veillette: chef environnement, Usine de Joliette, Bridgestone Canada Inc, Canada; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Michele Girardi, Scame Mastaf Spa, Suisio, Italy; David Mann, key account manager, SPC Rubber Compounding, UK. Well done to all and everyone else who had a go.
France Veillette - Using the end of the train to determine speed relative to the Brians, the train travel 50 meters while the Brians travel 10 meters. Therefore, the speed of the train is 5 times the speed of the Brians. While Brian T travels 30 meters, the train travels 30 meters + its length (L). time = distance/speed, then 30/x = (30+L)/5x. Therefore, the length of the train is 150-30 = 120 meters.
Andrew Knox - . If both Brian A and Brian T walk at, say 2 m/s, then it takes Brian A 10 s to walk 20 m and Brian T 15 seconds to walk 30 m. So the rear of the train travels 20 + 30 = 50 metres in the 5 s extra that Brian T has to keep walking after Brian A stops. So the train is travelling at 50/5 = 10 m/s.
From where Brian A and Brian T start from, the train front travels 150 m from the starting point in the 15 seconds it takes for the rear of the train to pass Brian T, who is now 30 m from the starting point in the direction the train is heading. So the length of the train is 150 - 30 = 120 metres..
Michele Girardi - Taking the origin in the position of the trainspotters, the equation of motion of the back of the train is X = v*t-L
Where v is the speed and L is the length. If the two people stop at times
t1 and t2, It's
v*t1-L = -20
v*t2-L = 30
summing L and dividing:
Since the people walk at the same speed, it's
t1/t2 = 20/30
Combining the two equations we get
20/30= (-20+L)/(30+L) whose solution is 120.
David Mann- Let the train length be L.
If we think about how much faster the train is than T, it covers L + 30 metres when T covers 30 metres. So the ratio is (L + 30)/30. For A the ratio is
(L - 20)/20. But as the spotters walk at the same speed then
(L + 30)/30 = (L-20)/20
Multiplying by 60 and solving gives L = 120
Any decent spotters should have been concentrating on the numbers though!