SOLUTION: Harry's motorboat can make an average of 8 miles per hour. One day he sets out for a trip, only to have the motor break down. Harry rows back at two miles an hour. When he reaches

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Question 835134: Harry's motorboat can make an average of 8 miles per hour. One day he sets out for a trip, only to have the motor break down. Harry rows back at two miles an hour. When he reaches his dock, he finds that he has been gone 5 hours. How far has he rowed?
The equation is 8x = 10 - 2x.
Tried this:
8x = 10 - 2x + 2x
8x + 2x = 10x
10x = 10
Also if anybody has some tips on recognizing equations in word problems. Thank You :)
Found 2 solutions by Edwin McCravy, Alan3354:
Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!
Harry's motorboat can make an average of 8 miles per hour. One day he sets out for a trip, only to have the motor break down. Harry rows back at two miles an hour. When he reaches his dock, he finds that he has been gone 5 hours. How far has he rowed?
Let D = the distance he motored out = the distance he rowed back.


               Distance     Rate    Time=Distance/Rate
Motoring out      D          8            D/8
Rowing back       D          2            D/2
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                            Total Time =   5

Time motoring out + Time rowing back = 5 hours

D%2F8%22%22%2B%22%22D%2F2 %22%22=%22%22 5

Multiply through by 8

         D + 4D = 40
             5D = 40
              D = 8 miles

Edwin

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Harry's motorboat can make an average of 8 miles per hour. One day he sets out for a trip, only to have the motor break down. Harry rows back at two miles an hour. When he reaches his dock, he finds that he has been gone 5 hours. How far has he rowed?
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The formula for the average speed of a round trip is
avg = 2*r1*r2/(r1 + r2)
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avg = 2*8*2/(8 + 2) = 32/10
avg = 3.2 mi/hr
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d = r*t = 3.2*5 = 16 miles round trip, 8 miles each way.
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I don't recommend trying to memorize a formula for all problems, but this one is similar to parallel flows, parallel resistors, etc, just with a factor of 2 for the round trip.
Notice it's independent of the distance.
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It was the basis of the Michelson-Morley experiment in the 1840's which showed that there was no effect of the "ether."
The existence of the ether was used to explain how light from the Sun could travel. The ether was the medium theorized.
The lack of effect disproved the existence of the ether, and it was put away in the closet with phlogiston.