Not Up To Speed

E4
Let's say you're driving your fancy stretch limo to a particular destination, wherever that is. The only assumption is that you're free to drive at any speed you choose, with no traffic jams or cops out to nab you. For the first half of the journey (and by half, I mean half the overall distance between the starting point and your finishing point) you drive at 20 kilometres per hour. 
You then realise that it's all taking way, way too long, and you're going to be late for a meeting. You, therefore, decide that you're going to increase your speed so that your overall average speed for the whole journey will be 40 kilometres per hour. How fast do you have to drive for the remaining part of your journey in order for your average speed for the whole journey to be 40 kmph? (Incidentally, the answer's the same, whatever the total distance of your journey.)
DEAR MS
 (The overbaked problem of last week was: "A PEAR, an APPLE, a LEMON and a BANANA all add up to an ORANGE. If each letter represents a number between 0 and 9 - both inclusive - solve the equation." - MS) 
Fruit-Cocktail-Dept:
The answer to PEAR + APPLE + LEMON + BANANA = ORANGE is 9782 + 89947 + 47530 + 180808 = 328067. It was a tough one even by Google standards and required sheer force. Phew! 
- Charanjit Singh Pardesi,
cspardesi@gmail.com 
This can be solved by using a computer running C language. After compiling and running the programme, the computer solves the equation denoted by the letters to allocate a corresponding number to the numeric variables that reads as N = 0, B = 1, R = 2, O = 3, L = 4, M = 5, G = 6, E = 7, A = 8 and P = 9. The numeric equation then transforms into 9782 (PEAR) + 89947 (APPLE) + 47530 (LEMON) + 180808 (BANANA) = 328067 (ORANGE), thereby solving the riddle. 
- Shashi Shekher Thakur,
shashishekher@yahoo.com 
(The second half-baked one was: "Okay so you've managed to get that peeled hardboiled egg into the bottle. How do you get it out now without breaking the bottle - MS) 
Egg-Planted-Dept:
(1) Place the bottle in a freezer. Once its temperature has dropped, invert the bottle so the egg blocks the neck from the inside and bring it out into room temperature. As the air inside the bottles heats up, it will push the egg out. (2) Invert the bottle so the egg blocks the neck and place it (suspend it actually) in an oven. As the air inside the bottle heats up, it will push the egg out. 
- J R K Rao,
(Email ID withheld on request.)
(The unbaked third problem was to get an unpeeled hardboiled egg into a similarly necked bottle without breaking the shell - plus how to get the contents of an egg out without breaking the shell. - MS)
Egg-Cell-Sheet-Dept:
To remove the contents of an egg without breaking the shell: Take a push pin and make a hole at the slimmer end of the egg. Insert a toothpick through the hole to break the yolk and mix it with the white of the egg. Make another hole at the wider end of the egg with a push pin. Using a straw, blow into the egg through the slimmer end. Thus without breaking the shell, the contents of the egg will come out. 
- Alifya Taher, talifya@gmail.com 
Dip the egg in vinegar till the shell softens and then do the peeled-egg operation. The egg easily goes into the bottle. To take out the contents of the egg, just insert a syringe through the shell and suck. 
- Sheikh Sintha Mathar,
sheikhsm7@gmail.com 
ENDGAME(S)
1. How can you show that, in any year, the same days of the month in March and November fall on the same day of the week?
2. A slice of uniform thickness of one centimetre is cut from a sphere of diameter 10 centimetres. What is the curved area of the slice? 
(Mukul can be reached at
mukul.mindsport@gmail.com)
 

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