Question 194738
Since the times are the same, the time is simply "t" for both equations.



So we have the equations


{{{2100=(400+w)t}}}


{{{1900=(400-w)t}}}




{{{2100=(400+w)t}}} Start with the first equation.



{{{2100/(400+w)=t}}} Divide both sides by {{{400+w}}}.



{{{t=2100/(400+w)}}} Rearrange the equation



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{{{1900=(400-w)t}}} Move onto the second equation



{{{1900=(400-w)(2100/(400+w))}}} Plug in {{{t=2100/(400+w)}}}



{{{1900(400+w)=(400-w)2100}}} Multiply both sides by {{{400+w}}}.



{{{1900(400+w)=2100(400-w)}}} Rearrange the terms.



{{{760000+1900w=840000-2100w}}} Distribute.



{{{1900w=840000-2100w-760000}}} Subtract {{{760000}}} from both sides.



{{{1900w+2100w=840000-760000}}} Add {{{2100w}}} to both sides.



{{{4000w=840000-760000}}} Combine like terms on the left side.



{{{4000w=80000}}} Combine like terms on the right side.



{{{w=(80000)/(4000)}}} Divide both sides by {{{4000}}} to isolate {{{w}}}.



{{{w=20}}} Reduce. 



So the speed of the wind is 20 mph.