## December 3, 2008

### Find the distance travelled

Two Buses enter in a tunnel 225 Km long, one of those buses
is travelling at 75 Km/h and at the same time another one
running at a speed of 37.5 Km/h from opposite directions.
As soon as they enter the tunnel a butterfly flying at
898 Km/h starts from one bus and heads toward the other one.
As soon as it reaches the other one it turns around and
heads back toward the first, going back and forth between
the buses until the buses collide in a fiery explosion
in the tunnel (the butterfly survives).
how far did the butterfly travel?

Secret Squïrrel said...

You could solve this by working out the reducing series of distances that the butterfly travels but the butterfly's speed has been chosen to make this horrible.

The trick is to realise that if you can work out how much time elapses before the crash, you can then more easily work out the distance that the butterfly travels.

Although we don't know how far each bus travels before the crash, they will travel a total of 225km (the length of the tunnel).

Each hour they will travel a total of 75 + 37.5 = 112.5 km. They will travel for 225 / 112.5 = 2hrs before they crash (see - the puzzle-setter chose numbers that actually give a nice round solution!).

So the butterfly will travel 898 * 2 = 1,796km before the crash.

Anonymous said...

wow that's complicated. but my question is how the f did the butterfly survive a big fiery explosion in a tunnel?????

Secret Squïrrel said...

If the butterfly is capable of surviving the heat generated by flying at 898km/h for 2 hours, I'm guessing that it is no ordinary butterfly!

Hmm, where's Evan telling us that the two buses could have been travelling in different lanes and that, although they both crashed, it wasn't into each other and that therefore the answer to this problem is "unknown"?