Question

A kayak is moving across a stream that is flowing downstream at a velocity of 4 km/hour. The kayak's velocity is 3 km/hour. What is the magnitude of the kayak's velocity relative to the river bank?

Answer 1

The question should clarify that 3 km/h is the kayak velocity with respect to the water, which would be the velocity in still water, rowing at the same power level. It is NOT the actual velocity as seen from shore, whjich is higher, since the kayer is paddling downstream.

Vkl = Vkw + Vwl, where:
Vkl is the velocity of the kayak with respect to land;
Vkw is the velocity of the kayak with respect to the water;
Vwl is the velocity of the water with respect to the land (i.e, the stream velocity of + 4 km/h).

Solve for Vkl

4 + 3 = ___ ?

Answer 2

In this case you must use the Pyth. Theorem.
so: 3^2 + 4^2 = c^2
9+16=c^2
c^2=25
c=5m/s

the answer is correct, but I cannot ensure you that the way to do it is 100%ly correct