# Rate of River Flowing

• November 27th 2012, 06:50 PM
feb6
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?
• November 27th 2012, 07:04 PM
MarkFL
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 $c$ be the speed of the current, then what is the speed going downstream and upstream? What range of values may $c$ have?

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