A boat heads directly across a river. Its speed relative to the water is 2.6 m/s. It takes it 355 seconds to cross, but it ends up 690 m downstream. How fast is the boat going relative to the bank of the river?

Vr = 3.24m/s

The boat is going 3.24m/s relative to the bank of the river.

Explanation:

The relative speed of the boat to the bank Vr is the resultant of speed of boat relative to the water Vb and the speed of boat as a result of the water current or wind Vw

Vr = √ (Vb^2 + Vw^2) ... 1

Given;

Vb = 2.6m/s

Vw = distance downstream/time = 690m/355s

Vw = 1.94m/s

From equation 1 above; substituting the values

Vr = √ (2.6^2 + 1.94^2)

Vr = 3.24m/s

The boat is going 3.24m/s relative to the bank of the river.