Problem 241: Gridlock
Dudley Keyes, lockkeeper of the Rosemount Quarry Canal, was baiting his fishing pole, always in the water by his side, when quarry manager Rockie D. Cutter stopped by.
“How’s the lock faring, Dudley?”
“Well, boss man, we’ve been havin’ a terrible time gettin’ enough water.”
“I thought you just filled a canal with water, and that was it,” Rockie said. “Is the problem evaporation?”
“Nope. That’s negligible. This here canal has a gargantuan lock; 50 ft long and 10 ft wide, so when them barges go up and down, you lose a heck of a lot of water every time you empty the lock chamber. And, the lock has a six-foot drop. I’ve been tryin’ to figure out just how much water those loaded barges use.”
“That’s easy – one lockful every time a barge goes through,” Rockie said arrogantly.
“Well, not exactly,” replied Dudley as he lit his corncob pipe. “Right after the mules pull a barge downstream, the lock is empty. So if one comes along going upstream, we ain’t gotta empty the lock.”
The granite curbing sections piled up on the barges have a 6 by 12 in. cross section and are 5 ft long. They weigh 160 lb to a cubic ft.
The barges are 40 ft long and 8 ft wide. The draft is 1 ft when they’re empty, but more when loaded. Every hour three barges go downstream, eighty curbings to a load, and three empty barges return upstream.
|Upstream:||5||25||35||minutes past the hour|
|Downstream:||15||45||55||minutes past the hour|
How many gallons of water per hour does the canal require?
Note: The locks are filled and emptied with sliding valves, or paddles built into the lock gates. Assume that water levels above and below the locks are constant. Water weighs 62.4 lb per cubic ft.
Solution to problem 240, October, 2000: Tunnel vision
Fun problem 239: Bombs away
Total entries: 173
Number correct: 160 (92%)
Winner: David Crockett, Morristown, Tenn.
David’s prize: Maple 6, a fully integrated analytical computation system.
Maple 6 combines the intelligence of Waterloo Maple’s symbolic computation algorithms with the reliability, accuracy, and power of the NAG numerical solver. Its math engine lets you define, solve, modify, optimize, and explore the mathematics or data in technical projects. This includes modeling and simulation, theoretical analysis, engineering design, and scientific application development.