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Kitchen Clock

Three short lessons on the maths of a dinner: working backward from the meal with one oven, why a roast twice as heavy takes less than twice as long, and what a kilo of carrots really costs once it is trimmed.

Spark & Whetstone · sparkwhetstone.org/learn/kitchen-clock · CC BY-NC-SA 4.0. Answers are at the end, so you can try each question first.

Lesson 1. Work backward from the meal

A dinner is a schedule with a fixed end. Start from the time you want to sit down and count each dish backward: the roast needs 90 minutes and 20 minutes resting, so it goes in 110 minutes before. With one oven the oven dishes cannot overlap, so they line up back to back, and the first of them sets the moment you must start.

Project planners call that chain the critical path. Everything else has slack: the salad can be made any time in the last hour. Children on LogicQuest order four dishes around one oven and find the single step that cannot wait.

Question. Dinner is at 6:00. The roast needs 90 minutes in the oven and 20 minutes resting after it comes out. When does it go in?

  1. 5:10
  2. 4:10
  3. 4:30

Say it back. In your own words: why do you plan a dinner from the end, and what does one oven change?

Lesson 2. Why a big roast takes less than twice as long

Heat gets into a roast through its surface, and the surface grows more slowly than the weight. Double the weight of a roast and its surface grows by only about 59%, so the cooking time grows roughly with the weight to the power of two thirds: about 1.59 times as long, not twice.

That is why cookbooks give a rule like “90 minutes plus 11 minutes a pound” rather than “so many minutes a pound”: a straight line with a head start fits the curve well over the sizes people actually cook. Children on SaffronLab compare the two rules and see where they agree.

Question. A roast twice as heavy as the one you usually cook needs roughly how much more oven time?

  1. About 10% more
  2. Exactly twice as long
  3. About 60% more

Say it back. In your own words: why does doubling a roast not double its time?

Lesson 3. What a kilo really costs

A kitchen buys by the as-purchased weight and cooks with the edible portion. The yield is the share that survives trimming: carrots at 78% yield give 780 grams of usable carrot from a kilo. Dry rice goes the other way, about 200%, because it drinks water.

So the price on the tag is not the price of what reaches the plate. A usable kilo costs the tag price divided by the yield: $2.00 a kilo at 78% is $2.56 a usable kilo. To serve 40 plates of 100 grams you need 4 usable kilos, which means buying a little over 5. ApprenticeDojo has older children run the same sums for a trade kitchen.

Question. Onions are $1.50 a kilo and 90% of each kilo is usable after peeling. What does a usable kilo cost?

  1. About $1.35
  2. $1.90
  3. About $1.67

Say it back. In your own words: why does a usable kilo cost more than the tag says?

At the table: The one-oven dinner on paper

Players: Two or more, ages 8 and up. You'll need: Strips of paper, a pen, a ruler or a long table edge as the clock.

  1. Write each dish on a strip, one centimetre for every ten minutes it needs, and mark the oven dishes.
  2. Lay the meal time at the right-hand end. Slide every strip so it ends there, then shuffle the oven strips so none of them overlap.
  3. Read off the earliest start. Ask: which strip could move without changing it, and which could not?
  4. Now add a dish and see whether the start moves. Talk about why it sometimes does not.

Answers

  1. 4:10 — 90 + 20 = 110 minutes. Counting 110 minutes back from 6:00 gives 4:10.
  2. About 60% more — Time grows with weight to the two-thirds power. 2 to the power ⅔ is about 1.59, so the bigger roast needs about 59% longer, not 100%.
  3. About $1.67 — $1.50 ÷ 0.90 = $1.67. The 10% that goes in the compost was paid for too.