Question 150817
Windspeed = {{{w}}}
{{{w = 10 mi/hr}}}
{{{p}}} = speed of plane is still air
{{{t}}} = time flying against and with the wind
Against the wind:
(1) {{{400 = (p - 10)*t}}}
With the wind:
(2) {{{500 = (p + 10)*t}}}
Multiply both sides of (1) by {{{5}}}
Multiply both sides of (2) by {{{4}}}
{{{2000 = 5*(p - 10)*t}}}
and
{{{2000 = 4*(p + 10)*t}}}
Since they both equal 2000, make them equal to eachother
{{{5*(p - 10)*t = 4*(p + 10)*t}}}
Divide both sides by {{{t}}}
{{{5*(p - 10) = 4*(p + 10)}}}
{{{5p - 50 = 4p + 40}}}
{{{p = 90}}} mi/hr
The speed of the plane in still air is 90 mi/hr
check:
(1) {{{400 = (p - 10)*t}}}
(1) {{{400 = (90 - 10)*t}}}
{{{400 = 80t}}}
{{{t = 5}}} hrs
and
(2) {{{500 = (p + 10)*t}}}
(2) {{{500 = (90 + 10)*t}}}
{{{500 = 100t}}}
{{{t = 5}}} hrs
OK