Math Problem: Rowing, Bottle (DRT)?

Question

My teacher says this is a fun distance-rate-time problem, and he refers to it as the "Napkin Problem" in case you know him. Here is the question:

A man rows upstream 1 mile. At point x, he drops a bottle into the river, which floats downstream. The man rows upstream 10 more minutes, then rows downstream. He and the bottle arrive at the dock at the same time. How fast is the river flowing?

I can't figure out how to get a speed and/or time out of this.
P.S. The bottle speed is obviously the speed of the river.

Answer 1

You are correct ... the bottle speed is the same as the river speed.

The boat rows upstream for 10 minutes, which is 1/6 of an hour.

The boat rows upstream at a speed of (boat speed - river speed).

The boat rows downstream at a speed of (boat speed + river speed)

The bottle travels downstream for 1 mile.

The boat travels downstream a distance of (1 mile + (boat speed)(1/6)) miles.

After the bottle is dropped, the time for the boat to travel upstream and then downstream is equal to the time the bottle travels downstream.



To assist you in setting up the equations to solve this, click on the source link I posted below. It explains a very similar problem that uses a dropped hat instead of a dropped bottle. But it does provide enough information for you to finish this problem.

Answer 2

Drt Math Problems

Answer 3

enable S = his velocity in nonetheless water, R = velocity of the river, D = distance rowed downstream, U = distance upstream Going downstream his velocity relative to land is S+R, going upstream it extremely is S - R. Now carry on with the formula Distance = velocity x Time, consequently Time = Distance / velocity Equate the two cases: D / (S + R) = U / (S - R) it is the final formula. Now plug interior the familiar numbers. 30 / (20 + R) = 12 / (20 - R) 30 (20 - R) = 12 (20 + R) 360 = 40 two R, consequently R = 360 / 40 two = 8.fifty seven mph to study, time downstream = 30 / (28.fifty seven) = a million.05 hr, upstream = 12 / (11.40 3) = a million.5 (quickly rowing and quickly river!)