Question 1059114

A boat moves 7 kilometers upstream in the same amount of time it moves 20 kilometers downstream. If the rate of the current is 5 kilometers per hour, find the rate of the boat in still water.
<pre>Let boat's rate be S
Average speed: {{{matrix(2,3, "Upstream:", S - 5, "km/h", "Downstream:", S + 5, "km/h")}}} 
Time boat takes to travel 7 miles upstream = {{{7/(S - 5)}}}
Time boat takes to travel 20 miles downstream = {{{20/(S + 5)}}}
We then get the following TIME equation: {{{7/(S - 5) = 20/(S + 5)}}}
20(S - 5) = 7(S + 5) ------ Cross-multiplying
20S - 100 = 7S + 35
20S - 7S = 35 + 100
13S = 135
S, or speed of boat in still water = {{{highlight_green(matrix(1,4, 135/13, or, 10&5/13, "km/h"))}}}