A plane cruises at 180mph in calm air If the plane flies 7 m

A plane cruises at 180mph in calm air. If the plane flies 7 miles with the wind in the same amount of time as it flies 5 miles against the wind, then what is the speed?

Solution

dist =vel *time
divide by vel
time=distance/velocity
Let x= wind velocity
given base velocity of 180
1) 7/(180+x) =time with wind
2) 5/ (180-x) = time against wind
given t1=t2
7/(180+x) =5/(180-x)
cross multiply
7(180-x)=5(180+x)
1260-7x=900+5x
subt 900, add 7x to each side
1260-900=5x+7x
360=12x
divide by 12
30 = x ANSWER (MPH)
check
7/(180+30)=5/(180-30)
7/210=5/150
.0333=.0333 ok