Question 975138

Here is my question:

A boat travels 12km upstream and back in 3 hours. If the speed of the current is 3 km/h throughout, make an equation and find the speed of the boat in still water.

Thank you very much!
<pre>Let speed of boat in still water, be S
Time taken to travel upstream: {{{12/(S - 3)}}}
Time taken to travel downstream: {{{12/(S + 3)}}}
Therefore, we have: {{{12/(S - 3) + 12/(S + 3) = 3}}}
12(S + 3) + 12(S – 3) = 3(S – 3)(S + 3) ----- Multiplying by LCD, (S – 3)(S + 3)
{{{12S + 36 + 12S - 36 = 3(S^2 - 9)}}}
{{{12S + 12S + 36 - 36 = 3S^2 - 27}}}
{{{24S = 3S^2 - 27}}}
{{{3S^2 - 24S - 27 = 0}}}
{{{3(S^2 - 8S - 9) = 3(0)}}}
{{{S^2 - 8S - 9 = 0}}}
(S - 9)(S + 1) = 0 
S, or speed in still water = {{{highlight_green(9)}}} mph	     OR	        S = - 1 (ignore)