Problema Solution
John Flies from Atlanta, GA to San Francisco, CA. It takes 5.6 hours to travel 2,100 miles against the head winds. At the same time, Debbie flies from San Francisco to Atlanta. Her plane travels with the same average airspeed but with a tailwind her flight only takes 4.8 hours. Write and solve a system of equations to determine the air speed of the plane and the wind speed.
Answer provided by our tutors
let
v = the speed of the plane in still air
w = the speed of the wind
d = 2,100 mi the distance from Atlanta, GA to San Francisco, CA
t1 = 5.6 h the time of the trip with the headwind
t2 = 4.8 h the time of the trip with tailwind
since speed = distance/time follows distance = speed*time
traveling with headwind the speed of the plane is: v - w
(v - w)*t1 = d
(v - w)*5.6 = 2100 divide both sides by 5.6
v - w = 375
traveling with tailwind the speed of the plane is: v - w
(v + w)*t2 = d
(v + w)*4.8 = 2100 divide both sides by 4.8
v + w = 437.5
by solving the system of equations:
v - w = 375
v + w = 437.5
we find:
v = 406.25 mph
w = 31.25 mph
click here to see the step by step solution of the system of equations:
the air speed of the plane is 406.25 mph.
the wind speed is 31.25 mph.