Question 1130823

A motorboat takes 5 hours to travel 100 km going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current? 

Rate of the boat in still water:

Rate of the current:
<pre>Let boat speed, in still water, be S, and speed of current, C
Then we get the following system of equations for the 2 speeds: {{{matrix(2,10, S - C, "=",  100/5, "======>", S - C, "=", 20, "------", eq, "(i)", S + C, "=", 100/2, "=====>", S + C, "=", 50, "-----", eq, "(ii)")}}}
2S = 70 ------- Adding eqs (ii) & (i)
Speed of boat, or {{{highlight_green(matrix(1,6, S, "=", 70/2, "=", 35, mph))}}} 
Speed of current, or {{{highlight_green(matrix(1,6, C, "=", 50 - 35, "=", 15, mph))}}}