Question 1042685
A small motorboat travels 13 mph in still water.
 It takes 2 hours longer to travel 60 miles going upstream than it does going downstream.
 Find the rate of the current.
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You are definitely on the right track. Here it is step by step anyway.
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let = the rate of the current
then
(13+r) = the effective speed down stream
and
(13-r) = the effective speed upstream
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Write a time equation, time = dist/speed
Time upstream - time downstream = 2hr
{{{60/((13-r))}}} - {{{60/((13+r))}}} = 2
multiply the equation by the common denominator
(13-r)(13+r)*{{{60/((13-4))}}} - (13-r)(13+r){{{60/((13+r))}}} = 2(13-r)(13+r)
Cancel the denominators, FOIL on the right (difference of squares)
60(13+r) - 60(13-r) = 2(169-r^2)
distribute
780 + 60r - 780 + 60r = 338 - 2r^2
Combine like terms to form a quadratic equation on the left
2r^2 + 120r - 338 = 0
simplify, divide by 2
r^2 + 60r - 169 = 0
Using the quadratic formula; a=1; b=60; c=-169, I got solutions of of
r = - 69.7
and
r = 2.7 mph is the rate of the current (the positive solution is all we want)
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See if this checks out by finding the actual time each way, Subtract and add the current from 13
60/10.3 = 5.825 hrs
60/15.7 = 3.822 hrs
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difference 2 hrs (discrepancy from me rounding off the original solutions)
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Did this make sense to you. Let me know in the comment CK