Question 56780
A plane flies 500 miles with the wind and 340 miles against the wind in the same length of time.  If the speed of the wind is 28mph, what is the speed of the plane in still air?
the distance formula is {{{d=rt}}} solve tihs for t and you have: {{{d/r=t}}}
Both our t's are the same so we're going to let t=t or d/r with the wind =d/r against the wind.
Let the rate of the plane be:x
Then the rate with the wind is: x+28
And the rate against the wind is: x-28
The distance with the wind is:500
The distance against the wind is: 340
The problem to solve is:
{{{500/(x+28)=340/(x-28)}}}
{{{500(x+28)(x-28)/(x+28)=340(x+28)(x-28)/(x-28)}}}
{{{500*cross((x+28))(x-28)/cross((x+28))=340*(x+28)*cross((x-28))/cross((x-28))}}}
{{{500(x-28)=340(x+28)}}}
{{{500x-14000=340x+9520}}}
{{{-340x+500x-14000=-340x+340x+9520}}}
{{{160x-14000=9520}}}
{{{160x-14000+14000=14000+9520}}}
{{{160x=23520}}}
{{{160x/160=23520/160}}}
{{{x=147}}}
The rate of the plane in still air is: 147 mph
Happy Calculating!!!