Answers

1. Answer:    16 miles

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   Explanation:

   x = time in hours spent going upstream

   5-x = remaining time in hours spent going downstream

   Those two quantities add to 5 hours total.

   Let’s find the expression for how far the fisherman went upstream

   distance = rate*time

   d = r*t

   d = 2x

   Do the same for the downstream portion

   d = r*t

   d = 8(5-x)

   d = 40-8x

   The values of d refer to the same distance because he came back to the starting point.

   Set those right hand sides equal to one another and solve for x.

   2x = 40-8x

   2x+8x = 40

   10x = 40

   x = 40/10

   x = 4

   5-x = 5-4 = 1

   He spent 4 hours going upstream, and the remaining 1 hour coming back downstream.

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   If he spent 4 hours going upstream at 2 mph, then he traveled d = r*t = 2*4 = 8 miles.

   The remaining 1 hour going downstream at 8 mph means he traveled d = r*t = 8*1 = 8 miles, which matches with the previous result. This confirms we have the correct one-way distance of 8 miles.

   Therefore, the total round trip distance is 2*8 = 16 miles

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