1.You drive to the store at 20 mph and return by the same route at 30 mph. Discounting the time spent at the store, what was your average speed?
2. Two trains travel toward each other on the same track, beginning 100 miles apart. One train travels at 40 miles per hour; the other travels at 60 miles an hour. A bird starts flight at the same location as the faster train, flying at a speed of 90 miles per hour. When it reaches the slower train, it turns around, flying the other direction at the same speed. When it reaches the faster train again, it turns around — and so on. When the trains collide, how far will the bird have flown?
3. A clock is observed. The hour hand is exactly at the minute mark, and the minute hand is six minutes ahead of it. Later, the clock is observed again. This time, the hour hand is exactly on a different minute mark, and the minute hand is seven minutes ahead of it. How many hours have elapsed between the first and second observations?
4. At McDonald’s you can order Chicken McNuggets in boxes of 6, 9, and 20. What is the largest number of nuggets that it is not possible to obtain by purchasing some combination of boxes?
5. Potatoes are made up of 99% water and 1% “potato matter.” Jack bought 100 pounds of potatoes and left them outside in the sun for a while. When he returned, he discovered that the potatoes had dehydrated and were now only made up of 98% water. How much did the potatoes now weigh?
6 and 7. You own a pet store. If you put in one canary per cage, you have one canary too many. If you put in two canaries per cage, you have one cage too many. How many canaries and cages do you have?
8. On a man’s tombstone, it is said that one sixth of his life was spent in childhood and one twelfth as a teenager. One seventh of his life passed between the time he became an adult and the time he married; five years later, his son was born. Alas, the son died four years before he did. He lived to be twice as old as his son did. How old did the man live to be?
9. 97 baseball teams participate in an annual state tournament. The champion is chosen for this tournament by the usual elimination scheme. That is, the 97 teams are divided into pairs, and the two teams of each pair play against each other. The loser of each pair is eliminated, and the remaining teams are paired up again, etc. How many games must be played to determine a champion?
10. A mountain goat attempts to scale a cliff sixty feet high. Every minute, the goat bounds upward three feet but slips back two. How long does it take for the goat to reach the top?
6. 4 canaries
7. 3 cages.