Question 168237
The times are the same for both trips, so
{{{t = d[1] / r[1]}}}
{{{t = d[2] / r[2]}}}
given:
{{{d[1] = 180}}} mi
{{{d[2] = 540}}} mi
{{{30}}} = mi/hr windspeed
Let {{{p}}}= ground speed of the plane
{{{t = 180 / (p - 30)}}}
{{{t = 540 / (p + 30)}}}
Since time is the same in both equations
{{{180/(p - 30) = 540 / (p + 30)}}}
Multiply both sides by {{{(p - 30)*(p + 30)}}}
{{{180*(p + 30) = 540*(p - 30)}}}
{{{180p + 5400 = 540p - 16200}}}
{{{360p = 21600}}}
{{{p = 60}}}
The ground speed of the plane is 60 mi/hr
check:
{{{180/(p - 30) = 540 / (p + 30)}}}
{{{180/(60 - 30) = 540 / (60 + 30)}}}
{{{180/30 = 540/90}}}
{{{6 = 6}}}
OK