Question 176889
Let {{{w}}}= the wind speed in mi/hr
Let {{{p}}}= the speed of the plane in still air in mi/hr
With the wind:
(1) {{{300 = (p + w)*(40/60)}}}
(2) {{{300 = (p - w)*(45/60)}}}
Set the right sides equal to eachother
{{{(p + w)*(40/60) = (p - w)*(45/60)}}}
Multiply both sides by 60
{{{40p + 40w = 45p - 45w}}}
Divide both sides by {{{5}}}
{{{8p + 8w = 9p - 9w}}}
{{{p = 17w}}}
Substitute this back in (1)
(1) {{{300 = (p + w)*(40/60)}}}
{{{300 = (17w + w)*(2/3)}}}
Multiply both sides by {{{3/2}}}
{{{450 = 18w}}}
{{{w = 25}}} mi/hr
and, since
{{{p = 17w}}}
{{{p = 425}}} mi/hr
The speed of the plane in still air is 425 mi/hr
The speed of the wind is 25 mi/hr
check:
(1) {{{300 = (p + w)*(40/60)}}}
(1) {{{300 = 450*(40/60)}}}
{{{450 = 450}}}
OK