SOLUTION: a motorboat traveled for 2 hours with an 8km/hr current. The return trip against the same current took 3 hours. Find the speed of the motorboat in still air.

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Question 536125: a motorboat traveled for 2 hours with an 8km/hr current. The return trip against the same current took 3 hours. Find the speed of the motorboat in still air.
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
D=RT and remember these problems often contain two situations. This one contains two situations.


1. D = rt where rate is r+8km/hr because it is moving with the current so the current adds to the speed. t = 2. Thus D=2(r+8)


2. The return trip was against the current, so the current works against the boat's speed (subtracts from it.) rate is r-8 and t=3. Thus D=3(r-8)


3. Because the boat traveled the same distance each time, those two equations both equal the same D, and thus are both equal to each other.


2(r+8)=3(r-8) (Multiply the numbers by each term in ().) 2r+16=3r-24


Subtract 2r from each side, add 24 to each side.


40=r.


The rate of the boat in still air (without any current working with or against it) is 40 km/hr.

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