Six Math Riddles
Generally, math puzzles and
riddles are solved by pure logic. Unlike lateral thinking puzzles
and other riddles, you usually don't have to get creative to
solve them. Still, there may be a surprising solution or two
here. Give yourself extra credit if you can do some of these
in your head.
1. Two planes headed towards each other, and are currently
440 miles apart. If one is going 240 miles per hour and the other
360 miles per hour, how far apart will they be four minutes before
they meet? (Extra credit if you can do this one without pen and
paper.)
2. Frank weighs half as much as John, and Hubert weighs three
times as much as Frank. Their combined weight is 720 pounds.
How much does each man weigh?
3. A certain investment doubles Joe's money every five years.
If Joe leaves all the money invested, in 40 years he'll have
384,000. How long will it take to have $384,000 if he starts
with twice as much money? How much money did he start with?
4. What is 50% heavier than a cubic foot of coal, but when
reduced in weight by 50% weighs less than a cubic foot of coal?
5. A plane travels at a speed of 400 miles per hour for 1200
miles, and then returns by the same route at a speed of 300 miles
per hour. What is the average speed for the total trip?
6. Bill can solve 32 math riddles per hour, and his friend
Sam takes three hours to solve the same number. If they both
work on them, how long will it take for them to solve 32 math
riddles?
Solutions
1. 40 miles apart. Combining their speeds we know that they
are closing the gap at 600 miles per hour, which is 10 miles
per minute (600 divided by 60 minutes in an hour). Therefore
they will go 40 miles in the last four minutes (4 minutes times
10 miles).
2. If John weighs twice as much as Frank, and Hubert three
times as much, dividing their total weight by six gives us Franks
weight (think x + 2x + 3x = 720). 720 divided by 6 tells us that
Frank weighs, 120 pounds, so John weighs 240 pounds and Hubert
360.
3. It would take 35 years if he invested twice as much. Think
of it this way; in the first scenario he has twice as much in
5 years, leaving 35 more to reach $384,000. He started with $1,500.
This is basic algebra: 384,000 = x (original investment) times
2 times 2 times 2 times 2 times 2 times 2 times 2 times 2 (eight
doublings). Thus $384,000 = 256x. Divide each side of the equation
by 256 and you get $1,500 = x, so we know he started with $1,500.
4. Anything that is 50% heavier than a cubic foot of coal
will weigh less when reduced in weight by 50%. Think of it this
way: 150 is 50% more than 100, but 50% of 150 (75) is smaller
than 100.
5. 343 miles per hour (342.857 to be more precise). Many people
answer 350 miles per hour, thinking they can just average together
400 miles per hour and 300 miles per hour. However, this doesn't
work, because although the distance is the same, the travel occurs
for longer times at the two different speeds. Thus, 3 hours are
spent going 400 mph on the first part, and 4 hours going 300
mph on the return. A total of 2400 miles are traveled in 7 hours.
2400 divided by 7 is 343 (rounded).
6. If Bill solves them three times as fast, he would be solving
24 of the 32 riddles, while Sam did 8 of them. Since 24 is 3/4
of 32, it would take 3/4 of an hour, or 45 minutes for the two
of them to solve the 32 math riddles.
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