Spring is in the air, so the coach provides a baseball puzzle and a swimming puzzle.
The players in the initial lineup of the Sluggers have jerseys numbered 1 to 9. Players in even-numbered batting positions have even-numbered jerseys, and each player’s jersey number is different from his or her batting order position. Players next to each other in the batting order have jersey numbers that differ by more than one. The Sluggers’ opponents have the same situation but a different batting order.
What are the batting orders of the two teams?
Team member Randall says, “I swam from our campsite this morning straight across the lake at my normal constant rate to the mouth of a stream flowing into the lake. I then swam upstream for a while to a lovely spot, took an hour for lunch, swam back downstream to the lake and straight back to our campsite at my normal rate. My total time away was exactly 3 1/2 hours.”
Sophie asks, “How far did you swim?”
“I don’t know any of the distances involved,” answers Randall, “but I do know my average speed downstream relative to land was 1.2 miles an hour and my average speed upstream relative to land was 0.6 miles an hour.”
Sophie says, “Since I know your normal swimming speed, that’s all I need to know.”
How far did Randall swim and how fast does he swim in the lake?
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Solutions to week 134
Maximization answer explained:
Let a = .1-4 = 10000 and b = .2-a = 510000. Then M = .3-b is the maximum. Ln(ln(M)) ≈ 16095. Ln(x) is the natural logarithm of x.
Links to all of the puzzles and solutions are on the Complete Varsity Math page.
Come back next week for answers and more puzzles.