Problems+of+the+Month

Interesting problems ...

Two asteroids are traveling towards each other at speeds of 10,000 miles per hour and 14,000 miles per hour, respectively. How far apart are the asteroids 2 minutes before their collision?

In the following decimal, if you were to keep track of how many 2’s there are, what would you count up to before you get to the one-hundredth 3? (The answer is not 1) 0.23223222322223 …

On Monday, Jimmy donated 10% of his money to a local food pantry. At noon, he spent $18 on a present for his dad. That afternoon, he used half of what was left to buy a video game. In the evening, he gave the rest of the money to his three sisters, who were pleased to receive $15 each. How much did Jimmy originally have?

Two horses approach each other along the same country road, one walking at 8 mph, and the other at 7 mph. When the horses are 15 miles apart, a horsefly leaves one horse and flies at 25 mph towards the other. No sooner does the fly reach that horse than it turns around (losing no time on the turn) and returns to the first horse. If the fly continues to fly back and forth between the approaching horses, how far has the fly flow when the horses meet?

The Earth’s Circumference A steel band is placed around the earth, snugly fit at the equator. (The equator is approximately 25,000 miles in circumference.) This band is cut, and a 36 inch piece of string is added to the steel band. This new circular band is placed around the earth, hovering above the earth’s surface, with its center being the center of the earth. A gap is created between the equator and this circular band. How wide is this gap?

Suppose you take a new job and the boss offers you a choice of: (A) $4,000 for your first year of work, and a raise of $800 for each year thereafter; (B) $2,000 for your first six months of work, and a raise of $200 every six months thereafter. Which offer would you take, and why?

Movie Ticket Problem A movie theater charges $7.00 per ticket. At that price, theater owners can expect to sell 1,100 tickets. They also found that for every 10 cent increase in ticket price, they will sell 20 fewer tickets. However, for every 10 cent reduction in the ticket price, they will sell an additional 20 tickets. What ticket price will maximize their income and what will their maximum income bHints: Income = (number of tickets sold) x (price per ticket) Diana designs stained-glass windows. She has a large supply of square glass window panes. Some panes are yellow and some panes are red. She wants to place them in windows like the one below in such a way that no two windows are the same, even when the design is rotated or reflected. How many different window designs can she create using any combination of red and yellow panes?



Farmer Jones has a whole bunch of chickens and cows on his farm. One day he was bored and counted 112 heads and 312 feet among all of his animals. How many chickens and cows does he have? Aaron, Beth, Candace, Darvel and Emil ran around a track as part of a fundraiser for their school. Aaron ran first, and then when he was tired, Beth ran. When Beth got tired, Candace ran, and so on. By the end of the fundraiser, they had run //a total of 30 miles//. Aaron and Beth combined ran 40 percent of the total distance. Beth and Candace combined ran 34 percent of the total distance. Candace and Darvel combined ran 40 percent of the total distance. Darvel and Emil combined ran 41 percent of the total distance. How far did each person run?