Mathematics Brain Teasers
1) Two trains, 200 km apart, are moving toward each other at the speed of 50 km/hour each. A fly takes off from one train flying straight toward the other at the speed of 75 km/hour. Having reached the other train, the fly bounces off it and flies back to the first train. The fly repeats the trip until the trains collide and the bug is squashed.
What distance has the fly traveled until its death?
There is a complicated and an easy way to calculate this cool math puzzle.
Think outside the box.
Ans: There is a complicated way counting a sequence. Or simply knowing that if the fly is flying for 2 hours still at the same speed of 75 km/h then it flies a distance of 150 km
2) A passenger train leaves New York for Boston traveling at the speed of 80 km/hr. In half an hour a freight train leaves Boston for New York traveling at the speed of 60 km/hr.
Which train will be further from New York when they meet?
Ans: Of course, when the trains encounter, they will be approximately the same distance away from New York. The New York train will be closer to New York by approximately one train length because they're coming from different directions. That is, unless you take "meet" to mean "perfectly overlap"
3) Let's play a game. If I went halfway to a town 60 km away at the speed of 30 km/hour, how fast do I have to go the rest of the way to have an average speed of 60 km/hour over the entire trip?
Ans: This one has not standard solution. You can't reach the desired average speed under the given circumstances. Easy math will prove that you can't make it at 90km/h or at any at any other speed.
4) The circumference of the Earth is approximately 40,000 km. If we made a circle of wire around the globe, that is only 10 meters (0.01 km) longer than the circumference of the globe, could a flea, a mouse, or even a man creep under it?
Ans: It is easy to compare old and new perimeter - original perimeter is 2xPIxR, length of wire is 2xPIx(new R) and find out that the result is about 1.6 m. So a smaller man can go under it and a bigger man ducks.
5) We know little about this Greek mathematician from Alexandria, called the father of algebra, except that he lived around 3rd century A.D. Thanks to an admirer of his, who described his life by means of an algebraic riddle, we know at least something about his life.
Diophantus's youth lasted 1/6 of his life. He had his first beard in the next 1/12 of his life. At the end of the following 1/7 of his life Diophantus got married. Five years from then his son was born. His son lived exactly 1/2 of Diophantus's life. Diophantus died 4 years after the death of his son.
How long did Diophantus live?
So the solution (x) is 84 years.
What distance has the fly traveled until its death?
There is a complicated and an easy way to calculate this cool math puzzle.
Think outside the box.
Ans: There is a complicated way counting a sequence. Or simply knowing that if the fly is flying for 2 hours still at the same speed of 75 km/h then it flies a distance of 150 km
2) A passenger train leaves New York for Boston traveling at the speed of 80 km/hr. In half an hour a freight train leaves Boston for New York traveling at the speed of 60 km/hr.
Which train will be further from New York when they meet?
Ans: Of course, when the trains encounter, they will be approximately the same distance away from New York. The New York train will be closer to New York by approximately one train length because they're coming from different directions. That is, unless you take "meet" to mean "perfectly overlap"
3) Let's play a game. If I went halfway to a town 60 km away at the speed of 30 km/hour, how fast do I have to go the rest of the way to have an average speed of 60 km/hour over the entire trip?
Ans: This one has not standard solution. You can't reach the desired average speed under the given circumstances. Easy math will prove that you can't make it at 90km/h or at any at any other speed.
4) The circumference of the Earth is approximately 40,000 km. If we made a circle of wire around the globe, that is only 10 meters (0.01 km) longer than the circumference of the globe, could a flea, a mouse, or even a man creep under it?
Ans: It is easy to compare old and new perimeter - original perimeter is 2xPIxR, length of wire is 2xPIx(new R) and find out that the result is about 1.6 m. So a smaller man can go under it and a bigger man ducks.
5) We know little about this Greek mathematician from Alexandria, called the father of algebra, except that he lived around 3rd century A.D. Thanks to an admirer of his, who described his life by means of an algebraic riddle, we know at least something about his life.
Diophantus's youth lasted 1/6 of his life. He had his first beard in the next 1/12 of his life. At the end of the following 1/7 of his life Diophantus got married. Five years from then his son was born. His son lived exactly 1/2 of Diophantus's life. Diophantus died 4 years after the death of his son.
How long did Diophantus live?
Ans: There is an easy equation to reflect several ages of Diophantus:
1/6x + 1/12x + 1/7x + 5 + 1/2x + 4 = xSo the solution (x) is 84 years.
Comments
Post a Comment