Puzzle n°39 (*) - Up and down the river

Some cats are pretty good swimmers, in particular Turkish Vans, did you know ?

One day, one of them set to water under a bridge and swam up the river over 1 km,
swimming against the current.
There, it met nose to nose a basket full of Easter eggs, gently floating, carried by the current of the river.

So stunned by this exceptional meeting, he immediately turned around to tell his friends
and swam down the river for 10 minutes before he realised he already passed the bridge !
He then turned around once more and, when he finally reached the bridge from where he started,
the basket was also just reaching it at exactly the same minute.

If our cat always swam at the same speed, what was the speed of the current ?

... I'm giving up ...