Hello antmanSuppose that the velocity of the boat relative to the water is , where and are constants. Then , since the speed of the boat (through the water, I assume that's what the question means) is a constant .

Then the velocity of the boat relative to the bank = velocity of boat relative to water + velocity of water relative to bank

, where is the position vector of the boat at time

and

, since when

time taken to cross

and

Solve for y by integrating. Then use when and .

This gives , and (from ) .

So the velocity of the boat is , and

Can you fill in the gaps?

Grandad