Question 962882
x=rate instill air; T=time; D=distance;y=wind speed
Rate into wind={{{360miles/4hrs=90mph}}}
Rate with wind={{{360miles/3hrs=120mph}}}
x+w=120mph
x=120mph-y
x-y=90mph Substitute for x.
(120mph-y)-y=90mph Subtract 120mph from each side.
-2y=-30mph Divide each side by -2.
y=15 mph ANSWER 1: The wind speed is 15 mph.
x=120mph-y=120mph-15mph=105mph ANSWER 2: The speed of the plane in still air is 105 mph.
CHECK:
Rate into wind:
4hrs=360mi/(x-y)
4hrs=360mi/(105mph-15mph)
4hrs=360mi/90mph
4hrs=4hrs
Rate with wind:
3hrs=360mi/(x+y)
3hrs=360mi/(105mph+15mph)
3hrs=360mi/120mph
3hrs=3hrs