Finding river speed when tugboat returns to drifting barge

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Garicup
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Homework Statement



A tugboat releases a barge and continues down the river for t = 64 min. Then it returns and finds the barge 3.9 km downstream from its initial position. Assuming that the speed of the tugboat was constant with respect to the water, the speed of the river is (in km/h)

Homework Equations



Relative Velocity ~~~
I think Vtw = Vtb + Vbw

tugboat wrt water (tw)
tugboat wrt barge (vb)
barge wrt water (bw)

The Attempt at a Solution



I thought the speed of the river would be velocity of barge wrt water?
except even that was true...i have no idea what to do with the information given
Looking for anything to point me in a starting direction. Not really sure where to start.
 
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Hi Garicup,

Garicup said:

Homework Statement



A tugboat releases a barge and continues down the river for t = 64 min. Then it returns and finds the barge 3.9 km downstream from its initial position. Assuming that the speed of the tugboat was constant with respect to the water, the speed of the river is (in km/h)


Homework Equations



Relative Velocity ~~~
I think Vtw = Vtb + Vbw

tugboat wrt water (tw)
tugboat wrt barge (vb)
barge wrt water (bw)

The Attempt at a Solution



I thought the speed of the river would be velocity of barge wrt water?

I believe the barge is just floating along in the water, so it's velocity wrt water would be zero.

So a good starting point is, how long does it take for the tugboat to reach the barge on its return journey? How can you determine that time?