# Boat travel

Debbie traveled by boat 5 miles up stream to fish in her favorite spot. Because of the 4 mph current, it took her 20 minutes longer to get there than to return. How fast will her boat go in still water?

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

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Let the boat's speed in still water denoted by x

Then, going upstream the speed is x-4

The time of travel is the distance of 5 miles (in hours) is Tu = 5/(x-4)

The speed downstream is x+4

And the time it takes to travel 5 miles is Td = 5/(x+4)

The time to travel downstream is 1/3 of an hour (20 minutes) shorter than going upstream.

Therefore:

Td + 1/3 = Tu

5/(x+4) + 1/3 = 5/(x-4)

Multiplying both sides by (x-4):

5(x-4)/(x+4) + (x-4)/3 = 5

Multiplying bit sides by (x+4):

5(x-4) + (x-4)(x+4)/3 = 5(x+4)

Multiplying both sides by 3:

15(x-4) + (x+4)(x-4) = 15(x+4)

expanding:

15x - 60 + x^2 - 16 = 15x +60

x^2 - 16 = 120

x^2 = 136

x = sqrt(136) = 11.66 mph

The speed of the boat in still water is 11.66 mph

I hope this helps

Thanks again,

Yinon

https://brainmass.com/math/basic-algebra/boat-travel-336442