Question 130565

Distance(d)=Rate(r) times Time(t) or d=rt; r=d/t and t=d/r

rate of the plane against the wind=220-20=200 mph
rate of the plane with the wind=220+20=240 mph
distance flown with the wind = distance flown against the wind
Time flying against the wind=d/200
Time flying with the wind=d/240

And we are told that these two times add up to 4 hours, so:

(d/200)+(d/240)=4  multiply each term by 4
d/50 + d/60=16
6d/300 + 5d/300=16
6d+5d=4800
11d=4800
d=436.36 mi---distance the plane can fly out and return safely (actually if I was the pilot I would shoot for about 420 mi out)

CK
436.36/200+436.36/240=4
3.99999999999999999999---~~4

Hope this helps---ptaylor