what is the speed of the wind

Question

Eddie is flying a jet against the wind on a 330 mile trip.  flying with the same wind speed, eddie could fly  a 550 mile trip in the same amount of time.  If Eddie's jet flies at 220 miles per hour in still air, what is the speed of the wind?   show work please

Answer 1

distance=rate*time

d=rt

let w=speed of wind

330=(220-w)*t

550=(220+w)*t

use the distributive property

330=220t-wt

550=220t+wt

add the two equations

880=440t (-wt+wt=0)

880/440=t

2 hours=t

substitute t=2 into either of the original equations

330=(220-w)*2

165=220-w

w=220-165

w=55 mph

550=(220+w)*2

275=220+w

w=55 mph

 

another solution:

330=(220-w)*t

330/(220-w)=t

550=(220+w)*t

550/(220+w)=t

330/(220-w)=550/(220+w)

cross multiply

330(220+w)=550(220-w)

72,600+330w=121,000-550w

330w+550w=121,000-72,600

880w=48,400

w=48,400/880

w=55 mph