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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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