Short Swim Math Problem...?

Question

...A two mile pier and a one nile pier extend perpendicularly into the ocean with four miles of shore between the two piers. A swimmer wishes to swim from the end of the longer pier to the end of the shorter pier with one rest stop on the beach. What is the shortest possible swim?

Answer 1

The above answer is close, but he forgot to take square root of the answers.

I got 4.69 miles. That is by using A^2 + B^2=C^2. Make two triangles. One is from long pier to half way down the shore and the other is from half way down shore to short pier. Find and add the hypotenuses.

If indeed it is a riddle, you don't have to swim. You could walk from the end of the long pier to the shore, then to the short pier, then down the pier.

Answer 2

The previous answers are wrong. Halfway down the shore is not the best stopping point, and rookard985 (answerer 3) took the wrong square roots - he should have got about 5.08 miles.

The answer is 5 miles exactly. He swims from the longer pier to a point on the shore 2 2/3 miles from it, then from that point to the end of the shorter pier. The hypotenuse of the first triangle, by Pythagoras, is 3 1/3 miles, and of the second triangle is is 1 2/3 miles.

The way to see the answer is to imagine the shorter pier flipped through 180 degrees. Then the shortest distance between the pier ends is a straight line, and you can work out where it crosses the shoreline. It is not halfway along, it is two-thirds of the way along.

Answer 3

If he starts from the two mile pier, and is immediately eaten by a shark, that would be the shortest possible under the facts given.

Answer 4

bh8153 is correct. If you flip the 1 mile pier to the mirror image, then you get a 3,4,5 triangle. This trick is also used for pool and billiard table, which is why there are dots at the table edge to help you.