As you hurry to catch your flight at the local airport, you encounter a moving walkway that is 84.0 m long and has a speed of 3.4 m/s relative to the ground. How long would it take you to cover the 84.0 m length of the walkway if, once you get on the walkway, you immediately turn around and start walking in the opposite direction with a speed of 1.5 m/s relative to the walkway?

Since you're walking opposite to the motion of the walkway, the speed

that you walk subtracts from the speed of the belt. Relative to the ground

(the floor of the building), your speed is

(3.4 m/s - 1.5 m/s) = 1.9 m/s

To cover the 84-m length of the walkway, it takes you

(84 m) / (1.9 m/s) = 44.2 seconds.

If you had just stood still and gone with the flow, it would have taken

(84 m) / (3.4 m/s) = 24.7 seconds.

Whereas, if you were willing to put forth the extra effort to keep

walking on the walkway, and had walked forward instead of

backward, then you would have moved at (3.4 + 1.5) = 4.9 m/s

relative to the stationary floor, and you would have covered the

full length of the walkway in only

(84 m) / (4.9 m/s) = 17.1 seconds.

In other words, once you jumped onto the walkway, you had

three options:

- - Stand still, for 24.7 seconds;

- - Walk forward, save 7.6 seconds;

- - Walk backwards, lose 19.5 seconds!

Being in a hurry, your decision to walk backwards was the worst choice.

It was not only totally inexplicable, but it also most likely irritated the other

people on the walkway, as they met you and had to all scrunch to one side

to let you go by in reverse.

It's not surprising that you had to hurry to catch your flight, I'm guessing

that you often miss them.