### Brain Teasers

# Tunnel Vision

A train passes through a long tunnel in the mountains. The train is 125 meters long, and travels at 40 kilometers per hour.

Just as the last car is completely inside the tunnel, a man begins walking from the end of the train to the front. He walks at 5 kilometers per hour and reaches the front of the train just as it emerges into the daylight.

How long is the tunnel?

Just as the last car is completely inside the tunnel, a man begins walking from the end of the train to the front. He walks at 5 kilometers per hour and reaches the front of the train just as it emerges into the daylight.

How long is the tunnel?

### Answer

Let x = the length of the tunnel in meters. The man travels x meters at 45 kilometers per hour (the combined speed of the train and his walking) in the same time that the train travels (x-125) meters at 40 kilometers per hour.The equation x/45 = (x-125)/40 solves to x=1125. Therefore, the length of the tunnel is 1125 meters.

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## Comments

Another approach is to note that 125 meters is one-eighth of a kilometer, so the man can walk 40 train-lengths in an hour.

This relates nicely to the speed of the train.

This relates nicely to the speed of the train.

Huh? Don't you do it like this?

Length of train / Speed of Man = Time Taken In Tunnel

125 m / 5000 = 0.025 hours

If the train is going 40 km an hour and was in the tunnel for 0.025 hours, then the distance of the tunnel is:

40km * 0.025 = 1km long

???

Length of train / Speed of Man = Time Taken In Tunnel

125 m / 5000 = 0.025 hours

If the train is going 40 km an hour and was in the tunnel for 0.025 hours, then the distance of the tunnel is:

40km * 0.025 = 1km long

???

Oh wait...is it because the train is only fully in when he starts walking, so you add the length of the train to get 125?

I did it the same way as Sane, and I also forgot to add the length of the train until I saw the answer. (1km is the distance the train travels while in the tunnel, so add the length of the train to get 1125m) Nice one, it caught me

Yeah caught me too. I did it in my head in about 10 seconds and came up with 1 km. When I read the answer I rethought my scenario an realised that the BACK of the train had traveled 1 km but the front of the train was still in the tunnel (just about to emerge).

It's little twists like this that turn a mundane arithmetic problem into a genuinely interesting teaser! Very good!

It's little twists like this that turn a mundane arithmetic problem into a genuinely interesting teaser! Very good!

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