Hello, SwissArmelle!

Both can be solved with the same set-up.

Here's #1 . . .

We will use: .

Let = speed of the swimmer (in km/hour).1. A swimmer can swim 4 km with the current in 24 minutes.

The same distance would take 40 minutes against the current.

Find the speed of the swimmer and the rate of the current

Let = speed of the current.

With the current, his speed is .

He swims 4 km in 24 minutes = hour.

We have: . .[1]

Against the current, his speed is

He swims 4 km in 40 minutes = hour.

We have: . .[2]

Add [1] and [2]: .

Substitute into [1]: .

Therefore, the swimmer's speed is 8 km/hr; the current's speed is 2 km/hr.