This Week From Bedtime Math: A Ferris Wheel for Boats

How can a wheel make a boat go airborne? Soar to new heights in today&s challenge from Bedtime Math!
By Laura Overdeck
Sep 23, 2014



Sep 23, 2014

What is Bedtime Math? A message from Laura: Bedtime Math is a pretty simple idea: We all know we should read to our kids at night, but what about math? My husband and I have done fun, mischief-loaded math problems with our kids at night for years, and when at age 2 our third child started hollering for his own math problem, we realized we were onto something:  In a world where so many people say, "Ewww, math!" we had created a household culture where kids don't just tolerate math, they actually seek it out. Now, every week, we'll be posting a new problem right here on Scholastic Parents!
Have you ever seen a canal? It's a water tunnel connecting two bodies of water that aren't at the same height, so boats can float from one lake or ocean to the next without tumbling down a waterfall. But if the two water levels are really different, we need a crazy machine like the Falkirk Wheel in Scotland. The Union Canal is a whole 115 feet higher than the Forth and Clyde Canal, so a "boat lift" has to pick up boats and bring them up there. The "gondola" (basket for the boat) fills with water, then the boat floats in, then the wheel turns like a giant Ferris wheel to lift the boat. At the same time, the other gondola at the top fills with water, too, and takes another boat down. The water and boats in each gondola weigh almost 300 tons — but because the two gondolas weigh almost the same, it takes almost no energy to turn them! That said, Ferris wheels for people probably have an even easier job.

Now that you've got the wheels turning in your head, see if your kids can come up with the answers to these math problems.

Wee ones: How many big grey LEGO wheels do you see in the LEGO model of the Falkirk Wheel?

Little kids: On each turn, the wheel uses only the energy needed to boil 8 kettles of water! If you already boiled 7 kettles of water to make steam to turn the wheel, how many more would you need to boil?  Bonus: If 100 people ride each boat on the wheel, how many people get to ride the 2 boats in total?

Big kids: The 2 gondolas together carry 500 metric tons of water and boat weight. How many tons does each gondola carry?  Bonus: Each gondola holds 66,000 gallons of water. Given that a gallon weighs about 8 pounds, about how many tons does the water alone weigh? (Assume short tons, which are 2,000 pounds each…and for a hint, divide by that number early on!)

The sky's the limit: Suppose you have a whole bunch of little boats on the Union Canal that want a ride to the bottom. They come in three sizes: 15-ton, 26-ton or 29-ton. If they need to balance one giant 120-ton boat coming up from the bottom, and you can load up to 6 little boats at once, what number and sizes of boats will balance the big boat most closely?
Wee ones: 3 LEGO wheels.
Little kids: 1 more kettle.  Bonus: 200 people.
Big kids: 250 metric tons.  Bonus: About 264 tons. To multiply 66,000 by 8 and divide by 2,000, divide by 2000 first to get 33, then just multiply that by 8.
The sky's the limit: The best choice is to load 4 26-ton boats and a 15-ton boat, giving you 119 tons. That's better than, for instance, 4 29-ton boats, which comes to 116 tons, or 5 15-ton boats plus another bigger one, which will fall short by even more.

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