Question 808958

the current in a stream moves at a speed of 9 mph. a boat travels 4 mi upstream and 4 mi downstream in a total of 4 hours. what is the speed of the boat in still water?


Let speed of boat in still water be S
Then average speed upstream = S – 9, and average speed downstream = S + 9


Therefore, {{{4/(S - 9) + 4/(S + 9) = 4}}}


4(S + 9) + 4(S – 9) = 4(S - 9)(S + 9) ------ Multiplying by LCD, (S – 9)(S  + 9)


{{{4S + 36 + 4S - 36 = 4(S^2 - 81)}}}


{{{8S = 4(S^2 - 81)}}}


{{{4(2S) = 4(S^2 - 81)}}}


{{{2S = S^2 - 81}}}


{{{S^2 - 2S - 81 = 0}}}


Using the quadratic formula, the speed of the boat in still water = {{{highlight_green(10.05538514)}}} mph


You can do the check!! 


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