Question 366321
Let {{{p}}} = the speed of the plane with no wind
Let {{{w}}} = the speed of the wind
Against the wind:
{{{d = (p - w)*t[1]}}}
With the wind:
{{{d = (p + w)*t[2]}}}
given:
{{{d = 600}}} km
{{{t[1] = 1.5}}} hrs
{{{t[2] = 1}}} hr
---------------------
{{{600 = (p - w)*1.5}}}
{{{600 = (p + w)*1}}}
and
{{{600 = 1.5p - 1.5w}}}
(1) {{{15p - 15w = 6000}}}
{{{600 = p + w}}}
(2) {{{p + w = 600}}}
Multiply both sides of (2) by {{{15}}} and
add (1) and (2)
(2) {{{15p + 15w = 9000}}}
(1) {{{15p - 15w = 6000}}}
{{{30p = 15000}}}
{{{p = 500}}}
The plane's speed with no wind is 500 km/hr.
The problem wants to know how long it takes to go
1200 km at that speed
{{{1200 = 500*t}}}
{{{t = 2.4}}} hrs
It takes 2 hrs and 24 min