Brain Teasers
Remember That Train Scene In 'Stand By Me'?
A man is standing on a railway bridge joining locations A and B. He is 3/8 the distance across, walking from A to B. He hears a train approaching behind him (from A's side); it is traveling 80 kph (that's kilometers per hour for you non-metric fans!) If he were to run back to A, he would meet the train at A. If he were to run to B, the train would overtake him at B.
How fast can the man run?
How fast can the man run?
Hint
You will never know exact distances in this problem, nor will you actually need to. Remember distance equals rate times time, or D = RT. I recommend drawing a picture to map out other distances, such as the man to A and B, respectively.Answer
Start by assigning some variables. We have three - the distance from the train to A, which I will call x; the distance from A to B, which I will call y; and the rate of the running man, in kph, which I will call z.The man is 3/8 the distance of A to B (which is y), so he is 3/8 y from A and 5/8 y from B (please note that the 'y' belongs in the numerator - the top of the fraction - not the bottom, so to be truly technical it is (3y)/8 and (5y)/8).
The time it takes the train to reach A is its rate divided by the distance, or 80/x. The time it takes the man to reach A would then be z/(3/8 y). Since they meet there, 80/x = z / (3/8 y). Solve for z, and simplify, to get z = 30y /x.
The time it takes the train to reach B is 80/(x + y), and the time it takes the man is z/(5/8 y). Again, since they meet there, 80/(x + y) = z/(5/8 y), and we get z = 50y /(x + y).
Set these two z-values equal to each other, so that 30y /x = 50y / (x + y), and cross-multiply. You then get 30xy + 30 y^2 = 50xy. Regroup to get 30y^2 = 20xy. Divide by 30y to get y = 2/3 x. Don't worry about y being 0 and making this pointless - y is a distance, and distances *can't* be 0, right?
So what does that do for us? Well, y is 2/3 of x. That means that the distance from A to B is 2/3 the distance from the train to A. Now, the man himself is 3/8 the distance from A to B (y), so he is 3/8 of 2/3 x away from A, or just 1/4 x away from A. So, in the time it takes the train to travel x, the man travels 1/4 x. So the man is running at 1/4 the speed of the train, or 20kph.
Feel like checking? OK. The train travels x and 2/3 x to get to B, or just 5/3 x. The man travels 5/8 y, or 5/8 (2/3 x), which is 5/12 x. And 5/3 divided by 5/12 is 1/4 again, so there you go.
Hide Hint Show Hint Hide Answer Show Answer
What Next?
View a Similar Brain Teaser...
If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.
Solve a Puzzle
Comments hidden to avoid spoilers.
Follow Braingle!