mensa teaser

[ddon]

A 330-yard long train, travelling at 30 mph, enters a two-mile long tunnel. How long will elapse between the moment the front of the train enters the tunnel and the moment the end of the train clears the tunnel?
Can you show workings please?

[dzug]

The tunnel is 1760x2 = 3520 yards long. Add the length of the tunnel gives3850 yards. Divide by 1760 gives 2.1875 miles as the distance the train has to cover.

Divide 30 by 2.1875 is 0.0729....hours or 4.375 minutes or 4 min 22.5 seconds.

If I haven't gone wrong......

[ddon]

Thanks. I got the same by working it out for the front of the train, then adding 60 / 52800 x 330. It just seemed clumsy and not a 'neat' answer so I thought I had gone wrong somewhere.

[ahornsey]

Being Mensa you should do it without a calculator!!

You're travelling at 30mph thats 1/2 mile/minute
So front of train entering to leaving is 4 minutes i.e distance * 2

That leaves 330/1760 of a mile for the end of the train to leave the tunnel.

Invert the fraction, 1760/330 = 5 110/330 == 5 1/3 or 16/3

Invert again = 3/16 of a mile
So time = 3/16 * 2 of a minute = 6/16 of a minute

In seconds = 360/16 seconds = 22 8/16 seconds = 22 1/2 seconds

Total time = 4' 22 1/2 ''