Question

An airplane flies 4800 miles into the wind for 15 hours. The return trip takes 10 hours. Find the speed of the airplane without a wind and the speed of the wind.

Answer 1

The speed of the airplane was 800 mph and the wind, 480 mph.

Explanation:

distance'd'/speed'v'=travel time't' and the distances are the same. The wind speed works against the plane upwind and helps the plane downwind, of course.

considering x=speed of airplane without wind

c=speed of wind

->Forward trip:

d/v=t

4800/(x-c)=15

320= x-c ---> eq(1)

->Return trip:

4800/(x+c)=10

480 = x+c --->eq(2)

Adding eq(1) and (2)

x-c + x+c = 320+ 480

x= 800 mph

eq(1)=> 320= x-c

c= 800 - 320

c=480mph

The speed of the airplane was 800 mph and the wind, 480 mph.