The current in a certain river flows at a constant rate of 6 miles per hour. A riverboat that travels at a constant rate of 18 miles per hour in still water, makes daily round trips on the river. How far upstream (against the current) does the riverboat transport passengers, if the round trip upstream and back takes 10 hours?
Doesn't solving for D give us the total distance of the round trip (80 miles)? The question asks us to just find the distance upstream, so I thought you would then divide the distance (80) by 2, giving us 40 miles each way?
The first thing to realize is that the rate of the boat upstream is 12 mi/hr. We have to account for the 6mph opposing current that is going to slow it down. The rate of the boat downstream is actually 18 + 6 = 24 mph since the current speeds up the rate of the boat. That's why we cant just divide by two. The upstream and downstream rates are different. The boat travels 12mph upstream and 24mph downstream.
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