Question 220956
The speed of a boat in still water is 10mph.  It travels 15 miles upstream and 15 downstream in a total of 4 hours. what is the speed of the current?


Let speed of current = C


Since speed in still water is 10 mph, then the speed to go upstream, against the current = 10 - C, and the speed downstream, with the current = 10 + C


Now, since total trip took 4 hours to travel in both directions of 15 miles each, and since Time = {{{D/S}}}, then we'll have: {{{15/(10 - C) + 15/(10 + C) = 4}}}


15(10 + C) + 15(10 - C) = 4 * (10 - C)(10 + C) ----- Multiplying by LCD (10 - C)(10 + C), in order to get rid of denominators


{{{150 + 15C + 150 - 15C = 4(100 - C^2)}}}


{{{150 + 15C + 150 - 15C = 400 - 4C^2}}}


{{{4C^2 = 400 - 300}}}


{{{4C^2 = 100}}}


{{{C^2 = 100/4}}}


{{{C^2 = 25}}}


{{{C = sqrt(25) = 5}}} mph


Therefore, speed of current = {{{highlight_green(5)}}} mph 

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Check
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Time upstream: {{{15/(10 - 5)}}} or {{{15/5 = 3}}} hours


Time downstream: {{{15/(10 + 5)}}} or {{{15/15 = 1}}} hour


Total time: (3 + 1) = 4 hours