Question

You have a 5 minute hour glass and an 8 minute hour glass. You need to cook something for exactly 9 minutes. How will you use the two hour glasses to determine the exact time? There is no way to determine where the halfway mark is with the hourglasses.

Help me please!

Answer 1

What is 3*8-3*5?

Answer 2

Not quite sure how to subtract times using an hourglass. Can't drain the 8' one and then subtract the 5' one.

However, if we do the following, I think it works. There may be more elegant ways:

The three columns show the running time, and the operations of turning glasses, with their remaining sand

time 8' 5'
0 8 5
5 3 0
turn 5'
8 0 2
turn 8'
10 6 0
turn 5'
15 1 0

Now you can start cooking, with 1' of sand in the 8' glass.
After 1 minute, turn the 8' glass and let it drain.