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