Question 320481
With a certain tail wind an airplane reached its destination, 630 miles away, in 1½ hours.
Flying back against the same wind, the plane took 15 minutes longer to make the trip.
 Find the wind speed and the plane's airspeed
:
Let s = plane's airspeed
Let w = wind-speed
:
From the given information: tailwind time = 1.5 hrs, against the wind = 1.75 hrs
:
write a distance equation for each trip; dist = time * speed
1.50(s + w) = 630
1.75(s - w) = 630
:
We can simplify here; 
divide the 1st equation by 1.5
divide the 2nd equation by 1.75
results
s + w = 420
s - w = 360
---------------adding eliminates w, find s
2s = 780
s = {{{780/2}}}
s = 390 mph plane airspeed
:
Find the wind using: s + w = 420
390 + w = 420
w = 420 - 390
w = 30 mph is the wind
:
:
Check solutions in original return equation
1.75(390 - 30) = 
1.75(360) = 630; confirms our solutions