Question 974580

Meg rowed her boat upstream a distance of 20 miles and then rowed back to the starting point. The total time of the trip was 12 hours. If the rate of the current was 4 mph, find the average speed of the boat relative to the water 
<pre>Let average speed in still water be S
Time taken to travel upstream: {{{20/(S - 4)}}} 
Time taken to travel downstream: {{{20/(S + 4)}}}
We then get: {{{20/(S - 4) + 20/(S + 4) = 12}}}
20(S + 4) + 20(S – 4) = 12(S – 4)(S + 4) ---- Multiplying by LCD, (S – 4)(S + 4)
{{{20S + 80 + 20S - 80 = 12(S^2 - 16)}}}
{{{40S = 12S^2 - 192}}}
{{{12S^2 - 40S - 192 = 0}}}
{{{4(3S^2 - 10S - 48) = 4(0)}}}
{{{3S^2 - 10S - 48 = 0}}}
(S – 6)(3S + 8) = 0
S, or speed of boat in still water = {{{highlight_green(6)}}} mph