Find the speed of the airplane in still air and speed of wind

Question

an Airplane takes 3hours to travel a distance of 2100 miles with wind. the trip takes 5 hours against the wind

Answer 1

distance = rate x time

 

R is the speed of the plane

S is the speed of the wind

 

With the wind:

  2100 = (r + s)*3

 

Against the wind: <--- Bob Segar fans like this equation

  2100 = (r-s)*5 

 

They are equal, as the distance is the same at 2100 miles

 

( r + s)*3 = (r-s)*5

 

3r + 3s = 5r - 5s

 

0 = 5r - 5s - 3r - 3s

 

0 = 2r - 8s

 

8s = 2r

 

r = 4s

 

The plane's speed is 4 times the speed of the wind

 

2100  = ( 4s + s)*3

 

2100 = 5s*3

 

2100 = 15s

 

s = 2100/15 = 140

 

The wind speed is 140 mph

The plane speed is 560 mph

 

With the wind: 3*(140 + 560) = 3 * 700 = 2100

Against the wind:  5*(560 - 140)  = 5*420 = 2100