Question 169265
Let the current be {{{s}}}
Let the rate of the boat with no current be {{{r}}}
With the current:
{{{d = (r + s)*t}}}
Against the current:
{{{d = (r - s)*t}}}
-------------------
Given:
{{{45 = (r + s)*5}}}
{{{45 = (r - s)*9}}}
Rewriting these,
{{{5r + 5s = 45}}}
{{{9r - 9s = 45}}}
Multiply the 1st by {{{9}}} and the 2nd by {{{5}}}
{{{45r + 45s = 45*9}}}
{{{45r - 45s = 45*5}}}
Add these equations
{{{90r = 45*14}}}
Divide both sides by {{{45}}}
{{{2r = 14}}}
{{{r = 7}}}
Substitute this back into a given equation
{{{45 = (7 + s)*5}}}
{{{9 = 7 + s}}}
{{{s = 2}}}
The rate of the current is 2 mi/hr
check:
{{{45 = (r + s)*5}}}
{{{45 = (7 + 2)*5}}}
{{{45 = 45}}}
------------
{{{45 = (r - s)*9}}}
{{{45 = (7 - 2)*9}}}
{{{45 = 45}}}
OK