Puzzle 1
At the local racetrack, Alex was testing the latest car.
During the eight test laps, Alex managed to average the first two laps at 100mph, the next two laps at 102mph, the next two laps at 140mph, and the last two laps at 150mph.
What was the average speed for the entire 8 laps?
Puzzle Copyright © Kevin Stone
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Hint
Remember that Time = Distance ÷ Speed, and try setting the track length to be a random length.
Answer
119mph.
Reasoning
It doesn't matter how long a lap is, so let's set the track length to be a random number, say 5 miles.
Using:
Time = Distance ÷ Speed
The first two laps took:
10 /100 hours
The second two laps took:
10 /102 hours
The next two laps took:
10 /140 hours
The final two laps took:
10 /150 hours
Therefore, the total time for the 8 laps was:
10 /100 + 10 /102 + 10 /140 + 10 /150 hours
= 1 /10 + 5 /51 + 1 /14 + 1 /15 hours
Looking at the denominators:
10 = 2 x 5
51 = 3 x 17
14 = 2 x 7
15 = 3 x 5
The lowest common multiple (LCM) of these numbers is 2 x 3 x 5 x 7 x 17 = 3570.
= 357 /3570 + 350 /3570 + 255 /3570 + 238 /3570 hours
= 1200 /3570 hours
= 120 /357 hours
= 40 /119 hours
The 8 laps were 40 miles, and using Speed = Distance ÷ Time:
average speed = 40 ÷ (40 /119 )
average speed = 40 x (119 /40 )
= 119 mph
Puzzle 2
Can you find every occurrence of the word JANUARY that appears in this grid (horizontally, vertically, or diagonally)?
The hint will reveal the number of times it occurs, but where are they?
Note: this puzzle is not interactive, and the letters cannot be selected.
Puzzle Copyright © Kevin Stone
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Hint
The word JANUARY appears 10 times.
Answer
The word JANUARY appears 10 times.
Puzzle 3
Below, you will find 10 seven-letter words, with only their endings remaining.
Can you find the words?
----igy
----aoh
----erg
----ynx
----lth
----mox
----ovy
----esh
----awe
----ipt
Puzzle Copyright © Kevin Stone
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Hints
The first letters of the words are: P, P, I, P, S, F, A, R, O, R.
Answers
----igy = prodigy
----aoh = pharaoh
----erg = iceberg
----ynx = pharynx
----lth = stealth
----mox = flummox
----ovy = anchovy
----esh = refresh
----awe = overawe
----ipt = receipt
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