You have 2 hourglasses–a 4 minute glass and a 7 minute glass. you want to measure 9 minutes.
How do you do it?
Start both the 4 and 7 minute HGs.
When the 4 runs out, you stop the 7 (with 3 minutes left).
You’re now at T+4.
Upend both again. There’s 4 to run on the 4 and 3 on the 7.
Stop when the 3 runs out.
You’re at T+7, the 4 has 1 minute, the 7 is empty.
Upend both again. You’ve 1 minute to go on the 4, and 7 on the 7.
Stop when the 4 runs out. You’ve an empty 4, and 1 minute in the bottom of the 7.
You’re at T+8.
Upend the 7. It will run for 1 minute and get you to T+9.
Another way to do it:
Start the 4-minute one and flip it each time it finishes. At the end of the fourth time through it will be T+16. Simultaneously start the 7-minute one and let it run out. At the point it runs out it will be T+7. It is thus 9 minutes from that point till the fourth time through for the 4-minute one.
Another method, this one involves some setup time, but simplicity at run time:
start 7 and 4 simultaneously
at end of 4, stop 7; it has 3 remaining
flip over 4 and continue 7
at end of 7, stop 4; it has 1 remaining
flip over 7 and continue 4
at end of 4, stop 7; it has 6 remaining
flip over 4 and continue 7
at end of 4, stop 7; it has 2 remaining
Setup is complete. You can discard the 4.
At the time you need to measure 9, you start the 7 (with 2 remaining in it)
After the 2 is gone, you flip it for the full 7
7+2=9
Another method.
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Run 7 and 4,
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When 4 empty turn it over, and let 7 continue.
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When seven is empty 4 has one minute remaining. (throw away 7 minute glass.)
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That one minute + 2 full 4 minute runs = 9 minutes.
Take both timers to Chef Troy.
Tell him you will give him these shiny, new, imported French cooking timers if he will tell you when 9 minutes has passed.
The way the problem is usually (and therefore IMHO correctly) stated, the time is 9 minutes from now. Note that Xerxes solves the usual version while Wendell Wagner and Bill H. solve a weaker version. (Wolfman is missing a step.)
I strongly urge puzzle posers to find out the standard/full statement of the problem first before posting.
ftg wrote
a) He did, which is to say he didn’t impose the restriction you desired.
b) Wolfman did not miss a step.
c) I like Wolfman’s solution better than my own. Fewer steps and disposal of the larger timer seems advantageous.
Bill H. wrote:
The way I see it he did. The 4 minute glass only runs out 2 times. 2x4=8. You only flip the glass twice, once when you start it, and once when it runs out. Yes, there will be 1 minute left when the 7 runs out, but it is still part of the second flip for the 4, so you can’t add it to 8. I could be wrong, and if so please explain it.
Thanks,
slackerboss
Here’s my interpretation of wolfman’s solution
start 7 and 4 simultaneously
at end of 4, stop 7; it has 3 remaining
flip over 4 and continue 7
at end of 7, stop 4; it has 1 remaining
Setup is complete. You can discard the 7.
At the time you need to measure 9, you start the 4 (with 1 remaining in it)
After the 1 is gone, you flip it for the full 4
After the 4 is gone, you flip it again for another full 4
1+4+4=9
Bill H.
After reading your post, and then going back to read wolfman’s post I see a word I did not before: The word “full”, that and it makes much more sense. Thanks
slackerboss
How do you stop an hour glass?
You turn it on its side
A way to do it in 9 minutes:
- start both timers
- when the 4-min. runs out out, turn it over, leaving the 7-min. running.
- when the 7-min. out, turn it over, leaving the 4-min. running. The 4-min. will have 1 minute left.
- when the 4-min. runs out, turn the 7-min. over. It will finish in one minute, at the 9-minute mark.
At T0 start both hourglasses.
At T4 when the 4minute is empty, flip it.
At T7 when the 7minute is empty, and the 4minute has 1 minute left, flip both.
At T8 when the 4minute is empty, and the 7minute has 1 minute left, flip the 7minute.
At T9 the 7minute will run out.
I think is is like xerxes solution except that the 7minute is not touched at T4.
hehe sublight you beat me to it 
except my step 3 was wrong, and yours was right, my solution should have read
At T0 start both hourglasses.
At T4 when the 4minute is empty, flip it.
At T7 when the 7minute is empty, and the 4minute has 1 minute left, flip the 7minute.
At T8 when the 4minute is empty, and the 7minute has 1 minute left, flip the 7minute.
At T9 the 7minute will run out.