Question 115079: She discovers that at full speed, the boat model can cover 1128 feet in 2 minutes. Suddenley she realizes that the boat is only 240 feet from the falls. She turns it around and runs it at top speed in the other direction. It looses. As the boat goes over the falls, she observes that 5 minutes passed since it was turned around. How fast did the boat move throught the water? How fast was the water flowing?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! I presume the problem statement means that the boat travels 1128 feet in 2 minutes in still water.
Let's begin with the basic formula that relates distance, rate, and time:  , or for our purposes here,  .
As soon as the boat turned around, even though it was going full speed ahead relative to the water around it, it was still moving, now backwards, toward the falls. But how fast was it traveling in that direction in relationship to the ground? Here's where we use the formula. We know that it turned around 240 feet from the falls and that it took 5 minutes to get from that point to the falls, so:
 =48 feet per minute in the direction of the falls.
Now, since the still water speed of the boat was given as 1128 feet per 2 minutes, the rate expressed as a unit of time would be 564 feet per minute, and that is how fast the boat moves through the water, regardless of the velocity of the current. But, since at full speed upstream, the boat was still moving downstream at 48 feet per minute, the current must have been fast enough to overcome the 564 feet per minute of boat speed PLUS the 48 feet per minute. Therefore, the velocity of the water must have been  feet per minute in the direction of the falls.
Hope that helps.
John
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