
Andrew M. answered 03/10/17
Tutor
New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors
I assume the 9 hours was the return trip with a tail wind.
d = rt distance = rate(time)
Using c = wind speed, r = plane speed:
With head wind:
distance = 1800
rate = plane speed minus wind speed = r-c
time = 16
1800 = 16(r-c)
16r - 16c = 1800 {equation 1}
With tail wind:
distance = 1800
rate = plane speed plus wind speed = r+c
time = 9
1800 = 9(r+c)
9r + 9c = 1800
r + c = 200 {equation 2}
16r - 16c = 1800
r + c = 200
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multiply 2nd equation by 16 and add equations
16r - 16c = 1800
16r + 16c = 3200
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32r = 5000
r = 156.25 mph
r + c = 200
156.25 + c = 200
c = 200 - 156.25
c = 43.75 mph
Check:
1800 = 16(r-c)
1800 = 16(156.25-43.75)
1800 = 1800
1800 = 9(r+c)
1800 = 9(156.25+43.75)
1800 = 1800
Answer fits the criteria given