Help understanding this velocity-time question

[sc8]

Homework Statement

A vacationer gets into his outboard motorboat and leaves a dock on a river bank for a day of fishing. Just as he turns upstream, he hears a splash but pays no attention and continues cruising at normal speed. Unfortunately, only 30.0 minutes later does he realize that his (fortunately watertight) lunchbox is missing. He then turns downstream, with the motor still set at cruising speed. Luckily, he sights his lunchbox floating down the river and retrieves it at a point 2.4 km downstream of the dock.
How long after turning around does he pick up his lunch?

Relevant Equations

v= d/t
Vae=Vab+Vb

The answer was revealed to be 30 minutes after turning around- but I'm having trouble understanding why. Can someone please explain this to me? Does it have something to do with relativity?

 

[Lnewqban]

Both, the boat and the lunchbox, are carried downstream by the river at similar rate, which is the velocity of the stream.
Unlike the boat, the lunchbox is floating; therefore, it has zero velocity respect to the stream.
Just imagine the problem with a river having no water movement: the trip back would last exactly the same time as the trip forward.

 

[haruspex]

Unlike the boat, the lunchbox is floating

I would hope the boat is floating too, but not just drifting.

imagine the problem with a river having no water movement

More to the point, consider it from the perspective of the lunchbox. The water is stationary, and the motorboat went at the same speed in both directions.

 

[Lnewqban]

Yes, the description given by @haruspex is more accurate; drifting is the correct word to use.
The problem considers the point of view of an observer who is standing on the shore of a river which water flows with certain velocity V.
The times would be exactly the same in the imaginary case in which the observer is walking with velocity V along the shore of a still lake in which the boat-lunchbox drama is developing.

 

[Merlin3189]

Isn't this just Galilean relativity? And you just sit on the lunchbox watching the boat drive away and come back again, and just ignore the banks sliding by.

 

[kuruman]

Isn't this just Galilean relativity? And you just sit on the lunchbox watching the boat drive away and come back again, and just ignore the banks sliding by.

Yes. It is the same situation as this: a person drops a coin in a windowless room, walks some distance $d$ away at then goes back to retrieve it, all at constant speed $v$ relative to the floor. The time required for each leg of the trip is clearly $t=d/v$. After he picks up the coin, the walls of the room are magically raised to reveal that he is on a raft floating in the river with the vacationer and his lunchbox farther downstream.