Additional Math Pages & Resources

Wednesday, May 4, 2011

Grand Complications, Part III

We are half-way through a Grand Complication Math problem - a situation that uses relatively simple math but involves many different calculations. I made up this term in recognition of the Grand Complication watches that some of my friends collect.

 A Vacheron Constantin Grand Complication

Yesterday we started to solve the Grand Complication Math problems related to moving. We calculated the volume of household goods, came up with a total, then selected a rental truck with a greater capacity than our volume of goods.

One additional factor in moving is related to using up all the cubic space in the truck. Unless you have lots of pillows and things you can toss up above, or you are an expert packer, it's not always possible to stack items. Therefore, much cubic volume in the truck is wasted.

We should also confirm we don't have items too long, or too wide or too high for the truck. That's not likely unless we are loading a playground set or some other strange items.

Now we just have to be sure we don't put too much weight in the truck.


NOTE: I went with a friend to collect soft drinks donated for a charity event. The forklift driver looked dubious when we showed up in a Ford F100 pickup. We thought the pallets of sodas would fit. He lifted the first pallet into the truck, and lowered the forks. The front wheels of our truck came up off the ground! Oops. The truck was rated to carry 1200 pounds of cargo - and we had tried to carry twice that! (120 cases/pallet x 20 lbs/case = 2400)

How do we calculate the weight of furniture? Luckily we don't have to weigh things as we are loading. We can use a rule of thumb developed by professional movers. They estimate density at 6 or 7 pounds per cubic foot for household goods. If you have lots of books, your load could weigh more. If you have lots of pillows, you're going to have a light load.

To finish up with our Grand Complication Math problem, let's estimate that the Romeros have 600 cubic feet of household goods. Their truckload will weigh about 4200 lbs.

The 14-foot moving truck from U-Haul holds 700 cubic feet and can carry 6000 lbs. That should be large enough to carry the Romero family's things.

Have my friends overloaded their Citroen station wagon with camping equipment?

PS Imagine that Mrs Romero is an elementary math teacher and she has a 35-student classroom set of Excel Math Lesson Sheets to put in the truck. How much will they weigh? Are they more or less dense than household goods?

Here is the answer:
  • Each curriculum set weighs 90 lbs
  • The set is split between 3 boxes
  • Each box is 14 x 9 x 9 inches or 1134 cubic inches
  • A cubic foot is 12 x 12 x 12 inches or 1728 cubic inches
  • Each box is 1134 ÷ 1728 = .66 or 2/3 of a cubic foot
  • The curriculum weighs 30 lbs per 2/3 cubic foot or 45 lbs per cubic foot
  • That's 7 times as heavy as household goods!