Noah and Emma, track stars with superb hearing, ran as fast as they could to catch up to the ice cream truck in the next town over. They averaged 6 miles per hour, then rested to enjoy their ice cream. They averaged 4 miles per hour over the same distance on the way back. Not counting the time they rested, what was their average speed?
4.8 miles per hour. 5 mph is tempting, but incorrect. Pick any distance, say 12 miles there and 12 miles back. They take two hours to cover the first 12 miles and three hours to cover the return trip. In 5 hours they covered 24 miles which is an overall average of 4.8 miles per hour.
I haven’t figured this out yet. Bad apple doesn’t really fit with the lowercase letters. They’re both vowels, but I don’t know if that’s relevant. The fourth one looks kind of like a hill, could it be apple hill?
Last winter I found myself locked out of my house because I couldn’t remember the 5-digit code to open the garage door. I used the following facts to get inside.
1. The second and third digits add up to 9.
2. The first digit is equal to the second digit cubed.
3. The sum of the third and fifth digits is the smallest number with exactly five divisors.
4. The fourth digit is equal to 6 times the second-to-last digit.
5. None of the digits repeat.
If we label each digit a, b, c, d and e, we get the following equations.
1. b + c = 9
2. a = b3
3. c + e = 16 (since 16 is the smallest number with five divisors – 1, 2, 4, 8 and 16).
4. d = 6 * d (The fourth and second-to-last digits are the same number, meaning d must be zero to satisfy the equation)
5. b must be zero, one or two (b can’t be three because that makes a=27, which isn’t a single digit). Zero and one result in duplicate digits (00907 and 11808 respectively) so the only remaining value for b is 2, giving us 82709 and warmth.
He and she both have one each, but every person has two. A citizen has three and a human being has four. A personality has five and an inhabitant of earth has six. What are they?