MEPX
Chapter 7 of 11All chapters
  1. 1How puzzles trick you
  2. 2All, some and none
  3. 3If, then
  4. 4Common fallacies
  5. 5Number sequences
  6. 6Words into equations
  7. 7Rate and work problems
  8. 8Elimination grids
  9. 9Knights, knaves and self reference
  10. 10Reading exactly
  11. 11Building the habit

Chapter 7 of 11

Rate and work problems

Machines, taps and painters.

Find the rate for one

Five machines make five widgets in five minutes, so one machine makes one widget in five minutes. A hundred machines working at the same time still take five minutes.

  • Reduce to one worker, one unit of time, then scale up.
  • Working together, rates add: two taps filling in 3 and 6 hours fill in 2 together.

Watch the units

Half the errors in rate problems are unit slips. Write minutes per widget or widgets per minute explicitly and the arithmetic follows.