Solve the problem.How do you measure 6 minutes with a 7-minute hourglass and a 5-minute hourglass? Assume that the hourglasses can only measure 7-minute and 5-minute intervals, respectively, and cannot be used to measure other time intervals.

Question

What will be an ideal response?

Answer 1

Answers may vary. One possibility: Start both hourglasses simultaneously. When the 5-minute hourglass runs out, immediately turn it upside down and start the timing of the 6-minute interval. There will be 2 minutes of time left in the 7-minute hourglass. When it runs out, immediately turn both hourglasses upside down. There will be 2 minutes of time left in the 5-minute hourglass (the 2 minutes that ran down before it was flipped). When it runs out, immediately turn the 7-minute hourglass upside down. There will be 2 minutes of time left in it (again, the 2 minutes that ran down before it was flipped). When it runs out, the timing of the 6-minute interval is complete  Incidentally, if you continue in this fashion, you can measure any interval of an even number of minutes using these two hourglasses. Of course, some intervals (e.g., 10 minutes, 14 minutes) can be measured much more simply using just one hourglass.