Hello, rcmango!

A boat is traveling relative to the water at a speed of 4.6 m/s due south.

Relative to the boat, a passenger walks toward the back of the boat at a speed of 2.0 m/s. Code:

* - - - *
| |
| ↑ |
| o |
| |
* *
\ /
\ /
\ /
*
↓

1) What is the magnitude and direction of the passenger's velocity relative to the water?

Also is this north or south? The boat is moving 4.6 m/s due south.

The man is moving 2.0 m/s due north.

His speed relative to the water is: .$\displaystyle 4.6 - 2.0 \:=\:2.6$ m/s due south.

2) How long does it take for the passenger to walk a distance of 27 m on the boat? At 2 m/s, it takes him $\displaystyle \frac{27}{2} \:=\:13.5$ seconds.

3) How long does it take for the passenger to cover a distance of 27 m on the water? Relative to the water, his speed is 2.6 m/s.

It will take him $\displaystyle \frac{27}{2.6} \,\approx\,10.4$ seconds.