# Thread: Rate of River Flowing

1. ## Rate of River Flowing

When paddling a canoe in moving water, you travel at a different rate than paddling in still water. The direction you are traveling determines whether you will go faster or slower.

The seeped at which the water is moving also makes a difference in the rate you are able to travel. The speed at which the water in a river moves varies with the amount of the water passing through it.

suppose you are a river guide who transports campers to a campground located 7 miles down river from a local ranger station. It is only 7 miles down river from a local ranger station. It is only accessible by non-motorized water craft. So you can use canoes. You transports campers and their equipment to the campground, unpack their belongings (which takes about 1 hour), and head back to the station.

you can paddle 3 miles per hour in still water, determine the time it would take to make a round trip to and from the campground for any current.

As a guide you want to be able to make the round trip in less than 10 hours so you can take campers to the campground, drop them off (which takes about 1 hour) and return to the ranger station before it gets dark. At what speed could the river be flowing if you are to successfully make the trip in the allotted time?

2. ## Re: Rate of River Flowing

To find the total time, we should consider that there are 3 parts to the trip, downstream, unpacking, and upstream.

We know unpacking time is 1 hour, and we know the distance of the trip is 7 miles. If we let $\displaystyle c$ be the speed of the current, then what is the speed going downstream and upstream? What range of values may $\displaystyle c$ have?

Once we have the speeds, how can we find the time?