How do you know when 30 minutes is up?

Question

You have exactly 30 minutes to get out of a room. All you have is a 9 minute hour glass and a 13  minute hour glass to count off exactly 30 minutes.  

Answer 1

Here is one potential solution...

 

Start both hour glasses at t=0, at t=9 flip the 9m hourglass back over...when the 13m hourglass ends for the first time at t=13, the 9m glass has 5m remaining....lay it on its side to freeze time for that glass, and flip the 13m glass over one more time...when it runs out again it will be t=26, at this time turn the 9m glass back on to drain the smaller amount of sand, which will take 4 more minutes and get us to t=30...when you should exit the room.

 

I believe there are other solutions, but this seems to save me from setting off whatever time sensitive explosive device must be guarding me and Indiana Jone's escape from the room!

Answer 2

The key is to note that 13-9=4 and 13+4+13=30.

 

At the beginning of the thirty minutes, start both hourglasses.

 

After nine minutes, the 9 minute hour glass will have emptied. Flip it over immediately.

 

In four more minutes, 13 minutes total will have elapsed. You will know because the 13 minute hour glass will empty. At this point, the 9 minute hourglass has four minutes worth of sand in its lower chamber. Flip it immediately.

 

It will take four minutes to empty. At that point, 17 minutes total have elapsed and there are 13 minutes left.

 

Start the 13 minute hourglass immediately. When it empties, the time is up.

 

I hope this helps.