# Math for Liberal Arts

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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.

• Math for Liberal Arts -

What is 3*8-3*5?

• Math for Liberal Arts -

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.

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