word problems

Question

An airplane flying into a headwind travels the 1830-mile flying distance between two cities in 3 hours. On the return flight, the airplane travels this distance in 2 hours and 30 minutes. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

 

Answer 1

let x=speed of plane
 c=speed of wind

x-c = speed without wind
x+c= speed with wind

distance=speed*travel time

 

2hr30min = 150 min=2.5 hr

 

1830 =(x-c)* 3

 

1830 =3x -3c   ___________ eq 1

 

1830 = (x+c)* 2.5

 

1830 =2.5x+2.5c ____________eq 2

 

multiply first equation with 2.5 and second equation with 3

4575 = 7.5x -7.5c  ___________ modified eq 1

5490 =7.5x + 7.5c ___________modified eq 2

 

add these 2 equation to eliminate c

 

10065 =15 x

 

x = 671 mph

1830 =3x -3c

3c =3x-1830

3c =3(671) -1830

3c =2013 -1830

3c =183

c = 61 mph

ans:
speed of plane=671 mph
speed of wind=61mph