Problema Solution
A Boeing 747 takes 30 minutes longer to fly from Denver, CO to San Francisco, CA than it takes to fly to Denver (a distance of 1200 miles). If the wind speed, from west to east, is 50 mph at cruise altitude, what is the speed of the airplane with no wind?
Answer provided by our tutors
let
v = the speed of the airplane with no wind
w = 50 mph the speed of the wind from west to east
San Francisco is West and Denver is East
t1 = the time flying from Denver to Sans Francisco (East to West)
the speed of the plane from Denver to Sans Francisco is v - w = v - 50
t2 = the time flying from San Francisco to Denver (West to East)
the speed of the plane from San Francisco to Denver is v + w = v +50
d = 1200 miles the distance
A Boeing 747 takes 30 minutes longer to fly from Denver, CO to San Francisco, CA than it takes to fly to Denver (a distance of 1200 miles)
t1 = t2 + 0.5 since 30 min = 0.5 hours
speed = distance/time
from Denver to Sans Francisco
d = speed*time
1200 = (v - 50)t1
from San Francisco to Denver
d = speed*time
1200 = (v + 50)t2
by solving the system of equations
t1 = t2 + 0.5
(v - 50)t1= 1200
(v + 50)t2 = 1200
we find
t1 = 2.21221 h
t2 = 2.71221 h
v = 492.443 mph
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the speed of the airplane with no wind 492.443 mph.