Question 172797
Let w=speed of wind and p=speed of plane



Note: 1 hour and 30 minutes = 1.5 hours (ie 1 and a half hours)



Against Wind:



Going against the wind will slow you down. So this means that the speeds plane against the wind is {{{r=p-w}}} 



{{{d=rt}}} Start with the distance rate time formula



{{{240=(p-w)1.5}}} Plug in {{{d=240}}}, {{{r=p-w}}}, and {{{t=1.5}}} (this is the time it takes to go against the wind)



{{{240/1.5=p-w}}} Divide both sides by {{{1.5}}}



{{{160=p-w}}} Divide.



{{{w+160=p}}} Add "w" to both sides to isolate "p".



So after isolating "p", we get {{{p=w+160}}}



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With Wind:



In contrast, going with the wind will speed you up. So this means that the speeds plane with the wind is {{{r=p+w}}} 



{{{d=rt}}} Start with the distance rate time formula



{{{240=(p+w)1}}} Plug in {{{d=240}}}, {{{r=p+w}}}, and {{{t=1}}} (this is the time it takes to go with the wind)



{{{240=p+w}}} Multiply



{{{240=w+160+w}}} Plug in {{{p=w+160}}}



{{{240-160=w+w}}} Subtract 160 from both sides.



{{{80=2w}}} Combine like terms.



{{{80/2=w}}} Divide both sides by {{{2}}} to isolate {{{w}}}



{{{40=w}}} Reduce



So the first answer is {{{w=40}}}. This means that the speed of the wind is 40 mph



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{{{p=w+160}}} Go back to the previously isolated equation



{{{p=40+160}}} Plug in {{{w=40}}}



{{{p=200}}} Add



So the second answer is {{{w=200}}}. This means that the speed of the plane is 200 mph



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Answer:


So the solutions are {{{w=40}}} and {{{p=200}}}


This means that the speed of the wind is 40 miles per hour and the speed of the plane is 200 miles per hour.