Engineer's Puzzle

The Puzzle: The train problem

The brain teaser that's impossibe to solve The Logic quiz for engineers gives the brain strain
Albert, 15/03/2016
Are we talking about an observer sat on the train or one sat on the embankment?  Read More

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Colin, an engineering manager at a component factory in Leeds, is on his way to go and see a customer ‘dahn sarf’ to try and build an ongoing partnership. Staring out the window he begins to wonder, when suddenly whoosh! Darkness descends as the train enters a tunnel... seconds pass as his eyes adjust and his ears pop. ‘How long will this last?’ He thought. And this got Colin thinking.

He gets out his phone and connects to the onboard wifi. He Googles the train type and finds it is 275 yards long. Another quick Google and he converts the figure to an SI unit. By this time he is out the tunnel so he opens up his maps app and GPS, and finds the name of the tunnel he just travelled through. He Googles that too, and finds it is one and a half miles long and it has a speed limit of 50mph.

He can now figure out what he initially wondered: ‘how many seconds elapse between the moment the front of the train enters the tunnel, to the moment the end of the train clears the tunnel?’


: 119.25s

This is how I did it.

First convert everything to SI units.

Train length: 251.46m

Tunnel length:2414.02m


Distance / time = speed

So, t = d/s = (2414.02+251.46) / 22.352 = 119.25s

Too easy? Why not email your puzzle to and put your wits against the intellect of Engineering Materials’ readership.

Justin Cunningham

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Engineer's Puzzle Entries
It would take 119.25 seconds.

Comment Sam, 02/05/2016
Actually, the text says, "‘How long will this last? He thought" i.e. the darkness in the tunnel, as perceived by him, so the length of the train is irrelevant.

Comment Andy, 16/03/2016
Are we talking about an observer sat on the train or one sat on the embankment?

Comment Albert, 15/03/2016
Biggest puzzle is why the engineer thinks he can get an answer correct to two decimal places with the information he's been given and the assumptions he's making. It's unlikely to take 119.25 seconds. Perhaps a little more, perhaps a little less depending upon the accuracy of the length of the train and tunnel measurements, perhaps a lot more if the train isn't actually travelling at the speed limit.

Comment Dr. Beeching, 15/03/2016
Actually the train never gets through the tunnel, it breaks down just outside Wakefield and our poor engineer ends up on a replacement bus service that arrives 5 hours late - in Cardiff...

Comment Nigel Hayes, 15/03/2016
Biggest puzzle is why the engineer wasted time converting to SI units in the first place...

Basically I did the same as Mr Aylett , the front of the train travelling at 24.44yd/s takes 108 second to traverse the 3960 yard tunnel. At the same speed it takes another 18.25s for the train to travel it's own length so rear reaches the same point hence the total elapsed time in 108 + 18.25 = 119.25s...

Comment Nigel Hayes, 15/03/2016
Why use SI when its all imperial - I am old enough to know that a mile is 1760 yards, so tunnel plus train is 2915 yards and speed of train is (50 x 1760)/ 60 x 60) yards per second. That cancels down to 880 / 36 yps so (2915 x 36)/880 = 119.25 seconds. Simples.

Comment Steve Clark, 15/03/2016
1.5 x 1.5 = 2.25
2.25 x 1760 = 3960
Someone stretched the tunnel ?

Comment reg dixon, 15/03/2016
To answer this question firstly convert 50mph to yards per second = 24.4444
then add the length of the length of the tunnel to the length of the train .in yards =
1.5 x 1760 = 3960 yds (tunnel length) + 275 (length of train) =4235 (total travel distance)
then divide this by speed of train = 4235 / 24.4444 = time for train to enter, travel through and exit the tunnel = 173.25 seconds

Comment Kelvin Aylett, 15/03/2016




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