John flies from Atlanta, Georgia to San Francisco, California. It takes 5.6 hours to travel 2100 miles against the head wind. At the same time, Debby flies from San Francisco to Atlanta. Her plane travels with 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 wind speed to distance for each traveler. Solve the system to find the airspeed. a. 406.25 mi/h c. 519 mi/h b. 408.45 mi/h d. 480 mi/h

Question

Mathematics

Jalen Irwin

4 July, 02:15

John flies from Atlanta, Georgia to San Francisco, California. It takes 5.6 hours to travel 2100 miles against the head wind. At the same time, Debby flies from San Francisco to Atlanta. Her plane travels with 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 wind speed to distance for each traveler. Solve the system to find the airspeed. a. 406.25 mi/h c. 519 mi/h b. 408.45 mi/h d. 480 mi/h

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Answers (2)

Know the Answer?

Pretty Lady · Answer 1

The answer is a. 406.25MPH

Rhianna Robertson · Answer 2

John:

distance = 2100 mi; time = 5.6 hrs; rate = d/t = 2100/5.6 = 375 mph

Debby:

distance = 2100 mi; time = 4.8 hrs; rate = d/t = 2100/4.8 = 437.5 mph

Let air speed be a and wind speed be w; then:

a+w=437.5 mph

a-w=375 mph

Solve the system to find the air speed.

Add the two equations:

a+w=437.5

a-w=375

becomes

2a = 812.5

a=812.5/2

air speed = 406.25 mph