Upstream Boat Rate Problem: "In 20 minutes while traveling upstream..."

jennie

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In 20 minutes while traveling upstream a river with a rate of 2 mph, the boat goes 528 miles. What is the rate of the boat in still water?
 
In 20 minutes while traveling upstream a river with a rate of 2 mph, the boat goes 528 miles. What is the rate of the boat in still water?
Please check your post, to make sure that you copied the exercise correctly.

Moving 528 miles in 20 minutes is way fast -- something like crossing the length of 7 soccer fields every second. :eek:

If the boat went for a whole hour, instead, that would still be 526 mph, in still water. (Note that I subtracted 2 mph from 528 mph because the boat's rate is reduced by the river water "carrying" the boat backwards at 2 mph.)

You know that we can express distance as a product. It's the product of rate (speed) and elapsed time.

rate * time = distance

This exercise asks for the rate in still water, so pick a symbol for that. Then subtract from it the speed of the river water moving opposite the boat. (Likewise, if the boat were moving downstream, with the water, then you would add 2 mph to the rate.)

distance = (r - 2) * time

If the given exercise actually says 528 miles in 20 minutes, you could do that science fiction version, and you could also do a regular speedboat version: change the distance to 5.28 miles

Next, 20 minutes is what fraction of a whole hour? That fraction is the time. (In the rate for the river water, the time unit is "per hour", so we need to convert the time to hours.)

Substitute the known values, and solve the equation for r. :cool:
 
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