Question 343360
Let {{{s}}} = speed of plane in still air
Let {{{w}}} = wind speed
Against the wind:
{{{3000 = (s - w)*6}}}
With the wind:
{{{3000 = (s + w)*5}}}
(1) {{{5s + 5w = 3000}}}
(2) {{{6s - 6w = 3000}}}
Multiply both sides of (1) by {{{6}}} and
multiply both sides of (2) by {{{5}}}
(1) {{{30s + 30w = 18000}}}
(2) {{{30s - 30w = 15000}}}
Add the equations
{{{60s = 33000}}}
{{{s = 550}}} km/hr
Plug this back into (1)
(1) {{{5*550 + 5w = 3000}}}
{{{2750 + 5w = 3000}}}
{{{5w = 250}}}
{{{w = 50}}} km/hr
check:
(2) {{{6s - 6w = 3000}}}
{{{6*550 - 6*50 = 3000}}}
{{{3300 - 300 = 3000}}}
OK