## Sand Glass

#### Problem

A sand glass is made from two conical glass sections, joined together by a thin glass tube. It is turned upside down and sand is allowed to pour from the top section into the bottom section. A sand glass has a carefully measured volume of sand placed inside it, such that it takes an exact amount of time for the sand to flow completely from one section to another. As the sand cannot escape the device it can be used over and over again, to measure a particular length of time accurately.

Two sand glasses have been designed to measure 9 minutes and 13 minutes respectively.

How would you use them to measure 30 minutes?

#### Solution

Start the 13 minute sand glass; once it has completed, we know that 13 minutes have elapsed. Turn it over to start it again, and at the same time start the 9 minute timer.
When the 9 minute timer has finished, turn it over to start it again; it will be a further 4 minutes before the 13 minute timer finishes.
Once the 13 minutes finishes again, 26 minutes will have elapsed in total and the 9 minute timer will have been been running for 4 minutes.
Now flip the 9 minute back over and when it has completed, 26 + 4 = 30 minutes will have passed.

What if you had a 9 minute and an 11 minute timer?

Investigate different timers to measure 30 minutes.

Problem ID: 226 (04 Jun 2005)     Difficulty: 2 Star

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