Question 965150
_______________________rate_______________time____________distance
AGAINST________________r-w_________________q_______________d
WITHWND________________r+w_________________p_______________d


KNOWN:
q=3.6
p=3.0
d=1800
UNKNOWN:
r, speed without wind
w, speed of the wind
The focus of the solution is for finding r.


{{{system((r-w)q=d,(r+w)p=d)}}}


{{{system(qr-qw=d,pr+pw=d)}}}


{{{-qw=d-qr}}}


{{{w=d/(-q)-qr/(-q)}}}


{{{w=-d/q+qr/q}}}


{{{highlight_green(w=qr/q-d/q)}}}





Substitute for w in the other equation:


{{{pr=d-pw}}}


{{{r=d/p-pw/p}}}


{{{r=d/p-(qr/q-d/q)/p}}}


{{{r=d/p-(qr/(pq)-d/(pq))}}}


{{{r=d/p+d/(pq)-qr/(pq)}}}


{{{r+(q/(pq))r=d/p+d/(pq)}}}


{{{r(1+q/(pq))=(d/p)(q/q)+d/(pq)}}}


{{{r(1+1/p)=(dq+d)/(pq)}}}


{{{r(p/p+1/p)=(dq+d)/(pq)}}}


{{{r(p+1)/p=(dq+d)/(pq)}}}


{{{r=(p/(p+1))((dq+d)/(pq))}}}


{{{r=(dq+d)/((p+1)(pq))}}}
maybe further steps, fully multiply denominator,


{{{highlight(r=(dq+d)/(p^2*q+pq))}}}


That is the formula for the rate of the airplane without the wind.
Now just substitute the values assigned and find the value for r.


This could have been easier if not done completely in symbols, but maybe you will have
other uniform travel rate exercises which are of the same form.