A small plane travels 520 miles with the wind in 3 hours 20

A small plane travels 520 miles with the wind in 3 hours, 20 mins (3 1/3 hours), the same time that it takes to travel 460 miles against the wind. what is the plane\'s speed in still air?

Solution

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=speed of plane in still air
And let w=windspeed
(With the wind, we add windspeed, against, we subtract)
r+w=520/(3 1/3)=520/(10/3)=1560/10=156 mph-----eq1
r-w=460/(3 1/3)=460/(10/3)=1380/10=138 mph---eq2
add eq1 and eq2
2r=294
r=147 mph-------------speed of plane in still air
substitute into eq1
147+w=156
w=156-147=9 mph ------speed of wind
CK
520/156=3 1/3 hr
460/138=3 1/3 hr