For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
04/01/2013

PROBLEM #1

You need to warm milk in a baby bottle from its initial temperature of 15 degrees centigrade to 25 degrees. You put the bottle in a pot of boiling water which stays at constant temperature of 100 degrees. The thickness and conductivity of the bottle are such that the initial rate of heat transfer is 85 degrees per minute. However heat transfer is proportional to the difference between the temperature of the milk and the water. How many minutes will it take to heat the bottle to 25 degrees?

PROBLEM #2

Water flows into a tank at a rate of 1 gallon per second. Water leaves the tank at a rate of 1 gallon per second for each 100 gallons in the tank. The tank is initially empty. How long will it take for the tank to fill with 50 gallons of water?

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Problems from 03/28/13

PROBLEM #1

Given only one of each letter in the alphabet, what are the smallest and largest numbers that you could write down?

SOLUTION 1
0 and 5000.

PROBLEM #2

A 1-metre stick is broken into two pieces at random. What is the length of the shorter piece, on average?

SOLUTION 2
0.25m.

Congratulations to Kishore Balsara, Suhas Joglekar and Saba Lateef, who were the winners of the last set of puzzles.

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