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A Trip to the Hospital is a puzzle in Professor Layton and the Miracle Mask.

Puzzle

A man went to visit his friend in the hospital. He got 500 meters from his front door before he remembered that he wanted some flowers. He went back to the flower shop and continued to the hospital. The flower shop is on a straight line between his house and the hospital, 800 meters from the hospital. Afterward, the man walked straight home, on the same road.

How many total meters did he walk between leaving home and returning?

Hints




Click a Tab to reveal the Hint.

Let's call the point where the man realizes he needs to buy flowers X. The outgoing and return journeys can be shown as: home -> X -> flower shop -> hospital -> home

Try drawing this route, being careful with the position of the flower shop.

First, the man walks 500 meters from home to point X. Next, he returns to the shop. Call this distance Y. Then he walks 800 meters from the shop to the hospital. That's the total outgoing journey.

On the return journey, he walks 800 meters from the hospital to the shop and then walks from the shop to his home. So, call this last distance Z, and the total is 500 + Y + 800 + 800 + Z

There are two distances you don't know: Y, from point X to the flower shop, and Z, from the flower shop to the man's home.

The shop is somewhere on the straight line between home and point X, and the distance from X to home is 500 meters. So the distance from X to shop (Y) plus that from shop to home (Z) must total...

As mentioned in Hint 2, the total distance is 500 + Y + 800 + 800 + Z.

From Hint 3, you can work out that Y + Z = 500.

The rest is just addition!


Solution

Incorrect

Too bad!

Try drawing a diagram of the entire route to the hospital via the shop and back home.

Correct

Correct!

The red line is the first 500 meters the man walked from home. The blue line is the return journey from the flower shop to the hospital, 2 x 800 = 1600 meters. The dotted lines show the original journey to the shop and the journey from the shop back home, which in total must be the same distance as the first 500 meters. So the total distance is 2600 meters.

A big thanks to http://www.youtube.com/user/LaytonKyouju

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