speed of the wind

Question

Against the wind a commercial airline in South America flew
510
miles in
3
hours. With a tailwind the return trip took
2.5
hours. What was the speed of the plane in still? air? What was the speed of the? wind?

Answer 1

v = speed in still air

w = wind speed

 

distance = speed * time

 

t = 3 hours against the wind, 2.5 hours with tailwind

 

Against wind:

 

(v-w)(3) = 510, which is same as v-w = 510/3 = 170

 

With tailwind:

 

(v+w)(2.5) = 510, which is same as v+w = 510/2.5 = 204

 

Solve above two equations as a system of two equations in two unknowns:

 

v - w = 170

v + w = 204

 

Add these two equations to get v:

 

2v = 374

v = 374/2 = 187

 

Now plug this v into either equation to get w, e.g. the top equation:

 

v - w = 187 - w = 170

w = 187 - 170 = 17

 

So speed in still air is 187 mph, wind speed is 17 mph.