Haretown and Tortoiseville are 72 miles apart. A hare travels at 7 miles per hour from Haretown to Tortoiseville, while a tortoise travels at 1 miles per hour from Tortoiseville to Haretown.

If both set out at the same time, how many miles will the hare have to travel before meeting the tortoise en route?

Solution:

The hare and the tortoise are together covering the distance at 8 miles per hour (i.e., on adding their speeds). So, they will cover the distance of 72 miles in 9 hours. Thus, in 9 hours, they will meet and the hare will have traveled 63 miles.

Alternative Solution through Equations:

Note that : Distance = Speed × Time

Let t be the time before the hare and the tortoise meet.In t hours, the hare will travel 7 t miles.In t hours, the tortoise will travel 1 t miles.

Now,7 t + 1 t = 72 So, t = 72 ⁄ 8 = 9 hours.

Thus, distance traveled by hare before meeting = 7 × 9 = 63 miles.

Case 1: Bird flies at a speed greater than that of the train

The train (at a speed of 60 miles per hour) travels 60 miles in 60 minutes. Therefore, the train travels from Atena to Barcena (78 miles) in 78 minutes.

Importantly, the bird makes the journeys continuously back and forth for this same amount of time (namely, 78 minutes).Thus, the total distance traveled by the bird = 70 miles per hour × 78 minutes = 70 × 78 / 60 miles = 91 miles.

Case 2: Bird flies at a speed less than that of the train

In 36 minutes, the bird travels 36 miles, the train travels 42 miles, and the two meet.Now, the train (which is traveling at a speed greater than that of the bird) will reach Barcena before the bird.So, the bird simply returns to Barcena (a return journey of 36 miles).Thus, the total distance traveled by the bird is 72 miles.

Case 1: Bird flies at a speed greater than that of the train

The train (at a speed of 60 miles per hour) travels 60 miles in 60 minutes. Therefore, the train travels from Atena to Barcena (78 miles) in 78 minutes.

Importantly, the bird makes the journeys continuously back and forth for this same amount of time (namely, 78 minutes).Thus, the total distance traveled by the bird = 70 miles per hour × 78 minutes = 70 × 78 / 60 miles = 91 miles.

Case 2: Bird flies at a speed less than that of the train

In 36 minutes, the bird travels 36 miles, the train travels 42 miles, and the two meet.Now, the train (which is traveling at a speed greater than that of the bird) will reach Barcena before the bird.So, the bird simply returns to Barcena (a return journey of 36 miles).Thus, the total distance traveled by the bird is 72 miles.

You are on your way to visit your Grandma, who lives at the end of the valley. It's her birthday, and you want to give her the cakes you've made.

Between your house and her house, you have to cross 7 bridges, and as it goes in the land of make believe, there is a troll under every bridge! Each troll, quite rightly, insists that you pay a troll toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake.

How many cakes do you have to leave home with to make sure that you arrive at Grandma's with exactly 2 cakes?

Answer2: At each bridge you are required to give half of your cakes, and you receive one back. Which leaves you with 2 cakes after every bridge.

Riddle 1) How can you add eight 8's to get the number 1,000? (only use addition)

The key to this math riddle is realizing that the one place must be zero. 888 +88 +8 +8 +8 =1,000

Digit Frequency

Part I. What digit is the most frequent between the numbers 1 and 1,000 (inclusive)?

To solve this riddle you don't want to manually do all of the math but rather try to figure out a pattern.

The most common digit is '1.' Can you figure out why? No hints until you try the next riddle because the next riddle is closely tied to this one.

Part II. What digit is the least frequent between the numbers 1 and 1,000?

0 is the least common digit even though 1,000 has three zero's !

Explanations for both riddles The digits 0 through 9 all follow the same pattern there is exactly 1 occurrence of each digit for every ten numbers.

For instance the digit 2 appears once between 10 and 19, at 12. And 2 appears once between, 30 and 39 at 32. However, each of the digits 1 through 9 also appear in other numbers in the tens and hundreds place

Again, let's look at 2 which appears in 20,21,22, 23, etc.. as well as 200,201, 202,203..

So to figure out how to answer the first riddle you had to see what distinguishes the number 1? Only that we are including 1,000 which would be the first '1' in a new series of ten! In other words, the digit 1 only has a single extra occurrence (301 occurrences) compared to 2 or 3 or 9 which each have exactly 300 occurrences.

The reason that zero has the least (BY FAR at only 192 occurrences) is because zero does not have any equivalents to 22, 33, 44, 222, 3333 etc..

You must cut a birthday cake into exactly eight pieces, but you're only allowed to make three straight cuts, and you can't move pieces of the cake as you cut. How can you do it?

Answer:Use the first two cuts to cut an 'X' in the top of the cake. Now you have four pieces. Make the third cut horizontal, which will divide the four pieces into eight. Think of a two by two by two Rubik's cube. There's four pieces on the top tier and four more just underneath it.

Math trivia questions and answers.

Q: What mathematical symbol did math whiz Ferdinand von Lindemann determine to be a transcendental number in 1882?A: Pi.

Q: What do you call an angle more than 90 degrees and less than 180 degrees?A: Obtuse.

Q: What's the top number of a fraction called?A: The numerator.

Q: What Greek math whiz noticed that the morning star and evening star were one and the same, in 530 B.C.?A: Pythagoras.

Q: What's a polygon with four unequal sides called?A: A quadrilateral.

Q: What's a flat image that can be displayed in three dimensions?A: A hologram.

Q: What number does "giga" stand for?A: One billion.

Q: What digit did Arab mathematician al-Khwarizmi give to the West around 800 B/B.?A: Zero.

Q: What word describes a number system with a base of two?A: Binary.

Q: How many equal sides does an icosahedron have?A: Twenty.

Q: What do mathematicians call a regular polygon with eight sides?A: An octagon.

Q: What T-word is defined in geometry as "a straight line that touches a curve but continues on with crossing it"?A: Tangent.

Q: What geometrical shape forms the hole that fits and allen wrench?A: The hexagon.

Q: What number is an improper fraction always greater than?A: One.

Q: What two letters are both symbols for 1,000?A: K and M.

Q: What's short for "binary digit"?A: Bit.

Q: What century did mathematicians first use plus and minus signs?A: The sixteenth.

Q: What number, a one followed by 100 zeros, was first used by nine-year-old Milton Sirotta in 1940?A: Googol.

Q: What handy mathematical instrument's days were numbered when the pocket calculator made the scene in the 1970s?A: The Slide rule's.

1. What is the next prime number after 7?

2. The perimeter of a circle is also known as what?

3. 65 – 43 = ?

4. True or false? A convex shape curves outwards.

5. What does the square root of 144 equal?

6. True or false? Pi can be correctly written as a fraction.

7. What comes after a million, billion and trillion?

8. 52 divided by 4 equals what?

9. What is the bigger number, a googol or a billion?

10. True or false? Opposite angles of a parallelogram are equal.

11. 87 + 56 = ?

12. How many sides does a nonagon have?

13. True or false? -2 is an integer.

14. What is the next number in the Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ?

15. 7 x 9 = ?

16. True or false? In an isosceles triangle all sides are unequal.

17. In statistics, the middle value of an ordered set of values is called what?

18. What does 3 squared equal?

19. True or false? -4 is a natural number.

20. 5 to the power of 0 equals what?

 Math Quiz Answers

 1. 11 2. The circumference 3. 22 4. True

5. 12 6. False 7. A quadrillion 8. 13

9. A googol 10. True 11. 143 12. 9

13. True 14. 55 15. 63 16. False (2 sides are equal)

17. The median 18. 9 19. False 20. 1

 Question: Two people dig cylindrical holes in the earth: one hole is two feet in diameter by two feet deep, and the other hole is one foot in diameter by one foot deep. The big hole is how many times the size of the small hole? is it twice as large, three times as

8 TIMES AS LARGE

Question: How many half-pints of a beverage could fill up a one-gallon container?

-16

Question: If you go out to eat at a restaurant in a foreign country, and you must pay a 15% service fee, followed by a 12% tax on everything, even the service fee, what actual exact percentage did you pay above the base price?

28.80%

Question: How long is a jiffy?

1/100th of a secondQuestion: What is a triangle with three congruent sides and three congruent angles better known as?

Equilateral Triangle

Question: If a family has three children, what's the probability that at least two of them are girls?

-50%

Question: This mysterious number, the base of a natural logarithm, is related to natural and exponential growth. What is this number called, and what is its decimal value?

"e" discovered by Swiss mathematician Leonhard Euler = approximately 2.72

Question: How many cubic millimeters make up a cubic meter? Express your answer as 10 to some power.

10 to the power 9

Question: Last year a dinner cost $32 and a bottle of wine cost $18. This year the cost of the dinner increased by 5% and the cost of the wine increased by 10%. What was the percent increase in the combined cost of the dinner and wine?.068 = 6.8 %

Question: An airplane departs at exactly 8:08:08 a.m. and arrives at its destination at exactly 3:03:03 p.m. To the nearest second, exactly what was the plane's travel time?

6:54:55 14:62:63- 8: 08:08

Question: Joe drank 1/3 of a glass of milk in one swallow, then drank 4/5 of the remaining milk in another swallow. What fraction of the original milk was left?

2/15

Question: There are approximately 1.6 million of these in every mile. What are they?

MILLI-METERSQuestion: A three digit number contains the digits 9, 5, and another digit. When this three digit number is reversed and subtracted from the original number, the result contains the same three digits as in the original number. What is the third digit?

Hide Answer

4Question: Steve has to be at work by 9:00 a.m. and it takes him 15 minutes to get dressed, 20 minutes to eat and 35 minutes to walk to work. What time should he get up?

Hide Answer

7:50amQuestion: Two people dig cylindrical holes in the earth: one hole is two feet in diameter by two feet deep, and the other hole is one foot in diameter by one foot deep. The big hole is how many times the size of the small hole? is it twice as large, three times as

Hide Answer

8 TIMES AS LARGEQuestion: If a bicyclist can drive down a one-mile hill three times as fast as she can ride back up the hill, and the round trip takes 20 minutes, how fast does she drive down the hill in miles per hour?

Hide Answer

12 MILES PER HOUR DOWN/ 4 MPH UP takes 4 minutes down and 15 minutes up.