TWO HOURGLASSES to measure 2 minutes

Problem

You have two sand hourglasses, one that measures exactly 4 minutes and one that measures exactly 7 minutes. You need to measure out exactly 2 minutes to boil an egg. Using only these two hourglasses, how can you measure out exactly 2 minutes to boil your egg? 

What if boiling eggs  take 9 minutes?

 

Solution

Boiling the eggs take 2 minutes

4 minutes : 7 minutes

#1:#2
4 : 7 Start both timers
0 : 3 After 4 min
4 : 3 Invert #1
1 : 0 After 3 min
1 : 7 Invert #2 and start cooking egg
0 : 6 After 1 min (egg half-cooked)
0 : 1 Invert #2 (7-6 = 1)
0 : 0 Stop cooking egg.

 

Total time from start: 7 min  

Boiling the egg taking 9 minutes

4 minutes : 7 minutes

#1:#2
4 : 7 Start both timers
0 : 3 After 4 min
4 : 3 Invert #1
1 : 0 After 3 min...#1 has 1 minute remaining
1 : 0  Leave #2 and start cooking egg
4 : 0 Invert #1. After 1 min (egg is 1 min-cooked)
0 : 0 Invert #1
4 : 0 Stop cooking egg.

 

1+4+4 = 9 minutes