Rowboat "on a Treadmill" Question
 

Say you are rowing a boat upstream as fast as you can. The water is flowing at 2 miles per hour, and your speed against the current is 4 miles per hour. Your rubber ducky blows off the boat, but you don’t notice. An hour later, you realize your ducky is gone. You turn around immediately and row back downstream as fast as you can. How long does it take for you to reach your ducky?

You don't reach the ducky ever because the rubber crocodile has eaten him

Roosevelt was visiting.
They hadn't fed the piranhas in days.

Bye-bye ducky, bye-bye.

upstream you are making 4mph against 2mph for 1 hour, so you've covered 4 miles (assuming the stream is really straight and you are measuring speed against a stationary reference, like land and not a changing reference like the water)
When you head downstream you are rowing at 6mph and the current is adding 2 mph for a total of 8mph. You would need to row for half an hour to return to the spot where your ducky fell off. An hour and a half has elapsed since the ducky fell and in that time the ducky has traveled, at 2mph, 3 more miles. You need to cover three miles to get to the ducky's current position. This will take you 22.5 minutes. in that time the ducky will have traveled another 3/4 of a mile. To close that gap and get within range you need to row for a few more minutes and use a full choke.

Somebody reads "Ask Marilyn".

How could you not notice the rubber ducky blowing off? He had curry for tea last night and the smell ... the smell ... and the air turned green, I mean a real vile shade of green.
Which way was the wind blowing?

I read Ask Marilyn today, too. ;)

Allowing a few simplifying assumptions...
no wind
uniform current
no eddies etc
The speed of the current is irrelevant since both boat and duck are in it. You've rowed away from Ducky for one hour, so to get back you must row towards him for one hour.

ur such a spoilsport

but he's got his ducks in a row

How far can a duck go, in a bathtub?

I thought I was the only one that read the Parade magazine in the newspaper. I mean, besides the Readers Digest large-type crowd.

I'm a little surprised you get the dead tree edition of the paper, Flint.

I thought I was the only one who did that. I just didn't get a chance to read the paper yesterday.

1.5 hours. You need to solve two equations. First: the distance the boat travels Db is 6 miles + the distance the duct travels Dd since the ducky has traveled 2 miles in an hour while the boat has traveled 4 miles in the opposite direction.
The second equation is the time of travel from the time the loss of the ducky was detected is the same for both. Since time = distance/speed, Dd/2 = Db/6. Note the boat speed downstream is 4+2 = 6 mph. Solving both equation will give the time of 1.5 hr during which the ducky has traveled 3 miles and the boat woild travel 1.5 hr x 6 mph = 9 miles (6+3).

Your first post is to do math everyone hated in elementary school. Welcome, Lilliput1. You're obviously our kind of people.