Question 933809
Questions 933811, 933810, and 933809 are the same fundamental problem as different examples.


<i>A vehicle traveling with the wind went w miles in t hours. Traveling against the wind, the vehicle could only go c miles in the same amount of time. Find the rate of the vehicle in calm air and the rate of the wind.</i>


The unknowns are r for rate in calm air, and n for the rate of the wind.


____________rate_______time_______distance
WITH______r+n________t___________w
AGNST____r-n__________t___________c


The equations are {{{(r+n)*t=w}}} and  {{{(r-n)*t=c}}}.
Solve for r and n.

{{{system(r+n=w/t,r-n=c/t)}}}

Add corresponding members to Eliminate(Method) n;

{{{r+n+(r-n)=w/t+c/t}}}
{{{r+r+n-n=(w+c)/t}}}
{{{2r=(w+c)/t}}}
{{{highlight(r=(w+c)/(2t))}}}.   This is one of the variables solved purely in symbols.


You can use Elimination again to solve for n.  Seeing that the system has coefficients of 1 on both variables, just subtract corresponding members.


{{{r+n-(r-n)=w/t-c/t}}}
{{{2n=(w-c)/t}}}
{{{highlight(n=(w-c)/(2t))}}}.  The other variable solved completely in symbolic form.


This question example uses values assigned to the given variables as
t=4, w=2060, c=1800.
Substitute them into the formulas and evaluate.