For The Mathematically Inclined

Two trains, one 500 meters long and the other 1000 meters long, are traveling in opposite directions on parallel tracks. The first train is traveling at 100 km/h and the other at 80 km/h. How long will it take for the trains to pass each other from the moment the locomotives are at the same point?

The figure shows right triangles ABC and ADC, angle ACB = 2.angle ACD, and DE perpendicular to AC. What is the ratio AB/DE?

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One morning is 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?

PROBLEM #2
Given n points drawn randomly on the circumference of a circle, what is the probability they will all be within any common semicircle?

SOLUTION 1

Congratulations to Abhimanyu Bhargava, who was the winner of the last set of puzzles.