ERJ Brainteaser - May
9 May 2025
Each month, ERJ sets a weekly brainteaser, with questions of varying degrees of difficulty. Readers supplying the most accurate (and stylish) answers are then considered for the prestigious Brainiac of the Month title.
Question 1: Trainspotting
Trainspotters Adam and Brian stand back-to-back next to a railway line. When the front of a train passes them, Adam starts walking in the opposite direction of the train, while Brian walks in the direction of the train. They walk at exactly the same speed, stopping precisely when the back of the train passes. If Adam walks exactly 40 metres, and Brian walks exactly 50 metres, how long is the train?
Answer: Right on track this week were: Bharat B Sharma, technical director, TWC Group (Rajsha Chemicals Pvt. Ltd), Vadodara (Guj) India; Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Sudi Sudarshan, principal consultant, Global Mobility Strategies, USA; Amparo Botella, responsable de Compras y Calidad, Ismael Quesada SA, Elche, Alicante, Spain. Well done to our select group, and everyone else who had a go.
SOLUTIONS
Bharat B Sharma
When the back of the train passes Adam, he and Brian have both walked 40meters.
Meaning Brian will walk 10 meters more when the train passes him. (50 m-40 m).
40 meters walked by Adam
50 meters walked by Brian
Total 90 meters that the back of the train travels in the same time that Brian walks 10 meters.
This means train is 90/10 (or 9 times) faster v/s. Adam and Brian.
In 40 meters walked by Adam, train will move 40x9 = 360meters (front of the train). Plus Alans distance of 40 meter (to reach end of the train) making total length of the train = 360+40 = 400 Meters.
Andrew Knox
If the train is travelling at speed V m/s and Adam and Brian both walk at the same speed v m/s then vt1 = 40 m or t1 = 40/v for Adam and t2 = 50/v for Brian. If the train is L m long, then equations are V = (L-40)/40/v = (L+50)/50/v. Solving for L gives L/40 - L/50 = 2, so 1.25 L - L = 100, or L = 400 m.
Sudi Sudarshan
Let s be the speed of Adam and Brian, L the train length and t the time for the back of thr train to pass Adam
When the back of the train passes Adam, he and Brian have already walked 40m and so the distance between them is 80m. In order for the back of the train to catch up with Brian it needs to travel 90m in the same time that Brian walks 10m.
So, trains speed = 9s
Time taken by Adam until the back of the train passed him = t = distance/time = 40/s
The train traverses (L-40 ) m during the same time at a speed of 9s
(L-40)/9s = 40/s
Cancelling s from both sides and simplifying,
L-40 = 360
L = 360+40 = 400 metres
Amparo Botella
Train speed = v
Walking speed = w
Time taken until the end of the train passes = t
For Adam: relative speed = v + w
t = v + w
And he walks 40 metres in that time:
40 = w t = v + w
For Brian (same direction): relative speed = v - w
t = v - w
And he walks 50 metres in that time:
50 = w t = v - w
40(v + w)=50(v - w)
40v + 40w = 50v - 50w
40w + 50w = 50v - 40v
90w = 10v v=90w/10 = 9W
L = 40(9w + w) = 400.
New teaser on Monday
