Question 989697



Traveling at full speed on a river, it takes 2 hours for a motorboat to travel 8 miles downstream and 4 miles back upstream. If the current's speed is 2mph, what is the maximum speed of the boat in still water?
<pre>Let speed of boat in still water be S
Total speed when travelling downstream: S + 2
Total speed when travelling upstream: S - 2
We can then form the following TIME equation: {{{8/(S + 2) + 4/(S - 2) = 2}}}
8(S - 2) + 4(S + 2) = 2(S + 2)(S - 2) -------- Multiplying by LCD, (S + 2)(S - 2)
{{{8S + 16 + 4S + 8 = 2(S^2 - 4)}}}
{{{12S + 24 = 2S^2 - 8}}}
{{{2S^2 - 12S - 24 - 8 = 0}}}
{{{2S^2 - 12S - 32 = 0}}}
{{{2(S^2 - 6S - 16) = 2(0)}}}
{{{S^2 - 6S - 16 = 0}}}
(S - 8)(S + 2) = 0
S, or speed in still water = {{{highlight_green(6)}}} mph    OR    S = - 2 (ignore)