Question 145239: john flies from atlanta georgia to san fransisco. it takes 5.6 hours to travel 2100against the head wind. at the same time debbie flies from san fransisco to atlanta, her plane travels at the same average airspeed, but with a tail wind, and her flight takes only 4.8 hours. write a system of equations that relates time, airspeed, and windspeed to distance for each traveler. sove the system to find the airspeed.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! john flies from atlanta georgia to san fransisco. it takes 5.6 hours to travel 2100against the head wind.
Time = 5.6 hrs ; distance = 2100 ; rate = 2100/5.6 = 375 mph
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the same time debbie flies from san fransisco to atlanta, her plane travels at the same average airspeed, but with a tail wind, and her flight takes only 4.8 hours.
Time = 4.8 hrs ; distance = 2100 ; rate = 2100/4.8 = 437.5 mph
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write a system of equations that relates time, airspeed, and windspeed to distance for each traveler. sove the system to find the airspeed.
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Let plane speed be "p" ; Let wind speed be "w"
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EQUATIONS:
p + w = 437.5
p - w = 375
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Add to get: 2p = 812.5
p = 406.25 mph (plane speed is still air)
Substitute to find "w":
406.25 + w = 437.5
w = 31.25 mph (wind speed)
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Cheers,
Stan H.
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