SOLUTION: Roy flies a plane against a headwind for 4977 miles. The return trip with the wind took 16 hours less time. If the wind speed is 8 mph, how fast does Roy fly the plane when there i

Question 1125875: Roy flies a plane against a headwind for 4977 miles. The return trip with the wind took 16 hours less time. If the wind speed is 8 mph, how fast does Roy fly the plane when there is no wind?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
time it took to go was t
return trip was t-16
distance=speed*time
two different times, same distance, speed is s-w against the wind, s+w with it.
so
4977=(s-w)*t; 4977=t(s-8)
4977=(s+w)*(t-16); 4977=(s+8)*(t-16)
t=4977/(s-8)
t-16=4977/(s+8); t=[4977+16(s+8)]/(s+8), adding 16 to both sides and putting it over a common denominator
4977/(s-8)=[4977+16(s+8)]/(s+8)
cross-multiply
4977(s+8)=4977(s-8)+16(s^2-64)
4977s+39816=4977s-39816+16s^2-1024
79632=16s^2-1024
80656=16s^2
s=71 mph ANSWER
63 mph against a headwind and takes 79 hours
79 mph with the wind and takes 63 hours, 16 fewer.

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