How Do You Calculate the Speed of a Boat Relative to Water?

[Elbobo]

Homework Statement

Two boat landings are 5.1 km apart on the
same bank of a streamthat flows at 3.4 km/hr.
A motorboat makes the round trip between
the two landings in 1.5 hr.
What is the speed of the boat relative to
the water? Answer in units of km/hr.

Homework Equations

The Attempt at a Solution

I tried to get the velocity of the water relative to the shore plus the velocity of the boat relative to shore to equal the velocity of the boat relative to the water.

That would give a right triangle with Vws and Vbs as the legs, and Vbw (what I'm trying to find) as the hypotenuse.

So I get sqrt ( (5.1 / 0.75)^2 + 3.4^2), which is 7.60 and wrong.

Please help me, I don't understand what I am doing wrong...

 

[Doc Al]

I tried to get the velocity of the water relative to the shore plus the velocity of the boat relative to shore to equal the velocity of the boat relative to the water.

velocity(boat/shore) = velocity(boat/water) + velocity(water/shore)

There's no need for any right triangles, since all velocities are in the same (or opposite) direction.

Hint: Use distance = speed*time
Set up that equation for when the boat's going upstream and for when its going downstream.