Question

An airplane
ies at a speed of 80 miles per hour in still air. On a day
when the wind is blowing from the north at 20 miles per hour, the airplane
ies 200 miles
straight north, then turns around and returns to its starting point. What is its average
speed on the round trip?

Answer 1

let u=80miles/h, v=20miles/h, s=200miles, w=average speed in miles/h,
t= total time in h, tp=time required in upstream in h.
so (u-v)tp=s and (u+v)(t-tp)=s and wt=s
=> tp=s/(u-v) and t-tp=s/(u+v) and w=s/t
so t= (tp)+(t-tp)=s[1/(u-v)+1/(u+v)]=s[u+v+u-v]/(u+v)(u-v)=2su/(u+v)(u-v)
so w=s/t=(u+v)(u-v)/2u=(80+20)(80-20)/2(80)=100(60)/160=37.5
so w=37.5miles/h

Answer 2

good try but not right answer

Answer 3

Flying against the wind, the plane has a ground speed of 80 - 20 = 60 mph. Flying with the wind, the plane has a ground speed of 80 + 20 = 100 mph. To fly the leg 200 miles into the wind takes 200 mi / 60 mi/h = 10/3 hr. To fly the return leg takes 200 mi / 100 mi/h = 2 hr. Total distance = 400 mi. Total time = 2 hr + 10/3 hr = 16/3 hr.

Average speed = 400 mi/ (16/3 hr) = 400*3/16 mph = 75 mph.

Answer 4

sorry there is an mistake. wt=2s not wt=s

let u=80miles/h, v=20miles/h, s=200miles, w=average speed in miles/h, t= total time in h, tp=time required in upstream in h.
so (u-v)tp=s and (u+v)(t-tp)=s and wt=2s => tp=s/(u-v) and t-tp=s/(u+v) and w=2s/t so t= (tp)+(t-tp)=s[1/(u-v)+1/(u+v)]=s[u+v+u-v]/(u+v)(u-v)=2su/(u+v)(u-v)
so w=2s/t=2(u+v)(u-v)/2u=2(80+20)(80-20)/2(80)=2*100(60)/160=2*37.5=75
so w=75miles/h