Question 159281
Remember: {{{Speed=distance/time}}}}, {{{t=distance/Speed}}} ----> working eqn
{{{SpeedTwinEngineAircraft=S[teac]}}}
{{{SpeedWind=S[wnd]}}}
According to our working eqn:
1st trip:
{{{500miles/(S[teac]+S[wnd])=4hours}}}
{{{S[teac]+S[wnd]=500miles/4hours}}}
{{{S[teac]+S[wnd]=125miles/hr}}} -----------------------------> eqn 1
2nd trip (going back):
{{{500miles/(S[teac]-S[wnd])=8hours}}}, see {{{S[wnd]}}} negative (-)->"against"
{{{S[teac]-S[wnd]=500miles/8hours=62.5miles/hr}}} -------------> eqn 2
In eqn 1, we get:
{{{S[teac]=125-S[wnd]}}} -------> eqn 3, and substitute in eqn 2:
{{{125-S[wnd]-S[wnd]=62.5mi/hr}}}
{{{125-62.5=S[wnd]+S[wnd]}}}
{{{62.5=2S[wnd]}}}
{{{cross(62.5)31.25/cross(2)=cross(2)S[wnd]/cross(2)}}}
{{{S[wnd]=31.25miles/hr}}}, SPEED OF WIND
For the aircraft, go back eqn 3,
{{{S[teac]=125-31.25}}}
{{{S[teac]=93.75miles/hr}}}
To check, go back eqn 1 or 2:
via eqn 1:
{{{93.75+31.25=125}}}
{{{125mi/hr=125mi/hr}}}
via eqn 2:
{{{93.75-31.25=62.5}}}
{{{62.5mi/hr=62.5mi/hr}}}
Thank you,
Jojo