Puzzle about hour glass

Question

there are 2 hour glasses - of 7 mins & 11 mins

how would you get time of 15 mins using both???

Answer 1

From Internet (Refer Source):"

It takes one turn of the larger glass. We start both glasses. After the smaller glass empties we start boiling one egg and continue watching the big glass. When the big glass runs out, the egg will have been boiling for 4 minutes. We turn the big glass and wait another 11 minutes. We get 4 + 11 = 15 with one turn of the big glass. Clearly, it is an absolute minimum.

In the generalized version, there are two hour glasses with capacities a and b (b > a) minutes. It is possible to measure 2b−a minutes by the above mentioned steps with a and b playing the role of 11 and 7.

Bogomolny refers to [15, #479] and to Quicky #1 [3, pages 190 and 199] as

the potential sources for this example. Note that in the second reference Gardner, who cites other sources, seems to have in mind a variation where the shortest time is to be found. However, because it fits the theme of our discussion, we will pursue only the version already proposed.

In our discussion, notice that both hour glasses were run concurrently and

without interruption. We restrict the scope of possible solutions beyond that of the original problem by stipulating that

(1) each hour glass, if used, must be used for an uninterrupted period of time by immediately turning it over each time it runs out during that period, and that

(2) the two hour glasses either must be started simultaneously or one started immediately after the other has run out for the last time.

Under these restrictions, each solution is simply the solution to a linear Diophantine equation.

"

AJM

Answer 2

Start both the 7 & 11 mins. hour glasses at the same time & after the 7 mins. is completed then 4 mins. will be remaining in the 11 mins. hg. After that again start 11 mins. hg & you get 15 mins.