Question 1165518

A boat traveled downstream a distance of 48 miles and then came right back. If the speed of the current was 12 mph and the total trip took 5 hours and 20 mins, find the average speed of beat relative to water.
<pre>Bemow you'll find the correct setup and CORRECT answer. 
Let boat's average speed be S
Then the time gong downstream = {{{48/(S + 12)}}}, and time spent going upstream = {{{48/(S - 12)}}}
We get the following TIME equation: {{{matrix(3,3, 48/(S + C) + 48/(S - 2), "=", 5&20/60, 48/(S + 12) + 48/(S - 12), "=", 5&1/3, 48/(S + 12) + 48/(S - 12), "=", 16/3)}}}
                                    {{{matrix(1,3, 3/(S + 12) + 3/(S - 12), "=", 1/3)}}} ---- Factoring out GCF, 16, in numerator
                                    3(3)(S - 12) + 3(3)(S + 12) = (S + 12)(S - 12) ------ Multiplying by LCD, 3(S + 12)(S - 12)
                                    {{{matrix(3,3, 9S - 9(12) + 9S + 9(12), "=", S^2 - 144, 9S - 108 + 9S + 108, "=", S^2 - 144, 0, "=", S^2 - 18S - 144)}}}
                                    0 = (S - 24)(S + 6)
                                    0 = S - 24     or      0 = S + 6
                                    Speed of boat, or {{{highlight_green(matrix(1,4, S, "=", 24, mph))}}}    or     - 6 = S (ignore)