# The barge ladder

You are the captain of a large barge and need to cross a canal in order to transport your barge from the sea to a lake above sea-level.

As you probably know, when you enter the lock, water is added in order to raise the water level until the intended above-sea level is reached.

As you know, this takes a long time.

Really bored, you start to do some math (as all bored people do):

Your barge is $9m\times3m$ long and $3m$ high, with $1m$ submerged in water.

A $1.75m$ long ladder is hanging at one side of the barge, and is used for climbing in the barge.

The lock is a $10m\times10m$ square and it's filled at a rate of $500$ liters per second.

How much time does the water take to reach the hanging ladder?

• I like this chestnut. Also, that it is a very small barge. – Engineer Toast Apr 22 '15 at 14:08
• @EngineerToast Shhh! Don't tell that to yourself or you'll lower your self-esteem! – Narmer Apr 22 '15 at 14:32
• Until I read the answers, I thought the ladder was hanging from the walls of the lock, not the barge. – user2357112 supports Monica Apr 23 '15 at 0:24

Infinity and beyond - the water will never reach the ladder.

Why?

Because your barge rises with the water level. Thus no matter how much the water rises the distance from the ladder to the water (the "height" of the ladder) will not change.

• Cant the lock have a ceiling? – Cthulhu Apr 22 '15 at 13:22
• @Cthulhu I've yet to see such one. Even if there is I doubt that a canal with locks with ceilings less than two meters when the lock is full will be of any practical value. – dmg Apr 22 '15 at 14:18
• Infinity is technically correct as it would eventually get high enough that the water started to freeze, except for around the barge where there's movement (at least for a short time). In which case the ice will rise. The atmospheric pressure may effect the submersion of the barge too. – Ash Burlaczenko Apr 22 '15 at 14:41
• @AshBurlaczenko We can draw some inspiration from here – dmg Apr 22 '15 at 16:36
• @Cthulhu - also, side walls that move inwards, preferably with spikes on. And a window in the ceiling so that the arch-criminal can watch your panic, despair and eventual demise. – Joffan Apr 23 '15 at 19:31

That water won't reach the ladder

Because

There will always be a 0.25m between the water and the end of the ladder, as the barge will always be only 1 m submerged in the water. I like how you provided all those numbers, that have nothing to do with the actual problem. Something that i also like to do.