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For The Mathematically Inclined

Anil Saigal
12/06/2009

PROBLEM # 1
One morning it starts to snow at a constant rate of 2 inches per hour. In the first hour 1 inch of snow melts away, in the second hour 1/2 inch melts away and in third hour 1/3 and so on.... How many inches on snow is on ground after 5 hours?

PROBLEM #2
One morning it starts to snow at a constant rate. Later, at 6:00am, a snow plow sets out to clear a straight street. The plow can remove a fixed volume of snow per unit time, in other words its speed it inversely proportional to the depth of the snow. If the plow covered twice as much distance in the first hour as the second hour, what time did it start snowing?


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Problems from 11/26/09

PROBLEM # 1

Find the slope of the line 5x - 5y = 7.

SOLUTION
1.

PROBLEM #2

A semicircle has "corners" on two concentric circles, tangent to the smallest (Figure 1 on right). What is its radius?

SOLUTION
2.28.

Congratulations to Sitaram Chandawarkar and Nikhil Nathwani, who were the winners of the last set of puzzles.



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