Question 155941

Distance(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r

Let r=rate(speed) of plane in still air
Let r1=rate (speed) of tailwind

With tailwind:  300=(r+r1)*1

300=r+r1-------------------------------eq1

Against tailwind: 300=(r-r1)*2

300=2r-2r1------------------------------eq2
multiply eq1 by 2 and then add it to eq2:

600=2r+2r1----------eq1a
300=2r-2r1-------------eq2

900=4r  divide each side by 4
r=225 mph---------------------------speed of plane in still air

substitute r=225 mph into eq1
300=225+r1  subtract 225 from each side 

300-225=225-225+r1 collect like terms

75=r1 or
r1=75 mph----------------------speed of wind

CK
300=(225+75)*1
300=300
and
300=(225-75)*2
300=150*2
300=300

Hope this helps--ptaylor