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Did You Work It Out? The Solution to Our Riddle from the E-News Issue No. 5, September 2015

Moving walkways make walking comfortable at airports. But what if this walkway was out of order?

If you travel by airplane you might be familiar with the moving walkways at airports. These walkways save you the effort of walking long distances and comfortably transport you through the airport.

Imagine that you are in are hurry as you are trying to catch your holiday flight. You jump onto the walkway, but instead of standing still, you decide to walk on the walkway to be even faster. While walking, you count that it takes you 66 steps to pass the walkway from start to end.

Two weeks later you come back from your holidays. The food at your holiday resort has been great and you have to admit that a little workout certainly would not hurt you. You challenge yourself by trying to walk the walkway against its direction of movement. The length and frequency of your steps stay the same as on your way to holidays. This time, it takes you a full 726 steps to conquer the walkway.

Take the previously mentioned figures into account and try to answer the following question:

If the walkway had been out of order, how many steps would it have taken you to pass it from start to end?

Solution

The way there: Travel saved through the motion of the walkway = walkway length - 66 steps

The way back: On your way back, you are 11 times longer on the walkway than on your way there (11 x 66 = 726)

On your way back, you spend 11 times longer on the walkway than on your way there (11 x 66 = 726).

When you walk the walkway in the opposite driving direction, you not only have to walk the length of the walkway, but in addition 11 times the distance that you saved on the way there.

Put into a formula, it looks like this:

11 x saved way + walkway length = 726

Length of saved way = walkway length - 66 (see the illustration "The way there" above)

When you enter this into the above equation, you get this result:

11 x (walkway length - 66) + walkway length = 726
11 x walkway length - 11 x 66 + walkway length = 726
12 x walkway length - 726 = 726
12 x walkway length = 1452

Walkway length = 121

Solution: You would have needed 121 steps to pass the walkway from start to end!