Timing 9 Minutes with Sand-Watches
Introduction
Dr. Johnson possesses two sand-watches: one measures 7 minutes, while the other measures 4 minutes. He needs to figure out how to accurately time a total of 9 minutes.
Step-by-Step Solution
To achieve this, Dr. Johnson should follow these steps:
1. **Start Both Watches**: Begin by turning both the 7-minute and 4-minute sand-watches simultaneously.
2. **After 4 Minutes**: When the 4-minute sand-watch runs out, immediately flip it over to start timing another 4 minutes.
3. **When 7-Minute Watch Runs Out**: Once the 7-minute sand-watch finishes, flip it over again. At this point, 1 minute of sand will still be in the 4-minute sand-watch.
4. **Final Minute**: Allow the remaining minute in the 4-minute sand-watch to finish. After it runs out, you will have 1 minute left in the 7-minute sand-watch.
5. **Total Time Calculation**: At this stage, you have timed 4 minutes (from the 4-minute sand-watch) plus an additional 3 minutes (from the 7-minute sand-watch) and finally 2 minutes (the last minute of the 7-minute watch). This sums up to a total of 9 minutes.
Conclusion
By effectively utilizing both sand-watches, Dr. Johnson can accurately measure a total of 9 minutes through this method.