Question 175912
Let {{{p}}}= speed of plane in still air
Let {{{w}}}= speed of the wind
with the wind:
(1) {{{d = (p + w)*t[1]}}}
Against the wind:
(2) {{{d = (p - w)*t[2]}}}
given:
{{{t[1] = 7}}}hrs
{{{t[2] = 14}}}hrs
{{{d = 560}}}mi
rewriting (1) and (2),
(1) {{{560 = (p + w)*7}}}
(2) {{{560 = (p - w)*14}}}
------------------------
(1) {{{7p + 7w = 560}}}
(2) {{{14p - 14w = 560}}}
Multiply (1) by {{{2}}} and add to (2)
(1) {{{14p + 14w = 1120}}}
(2) {{{14p - 14w = 560}}}
{{{28p = 1680}}}
{{{p = 60}}} mi/hr
(1) {{{560 = (60 + w)*7}}}
{{{560 = 420 + 7w}}}
{{{7w = 140}}}
{{{w = 20}}}mi/hr
The plane's speed in still air was 60 mi/hr
the wind speed was 20 mi/hr