Problema Solution
A plane carried enough fuel for 20 hours of flight at an airspeed of 150 mph. How far can it fly into a 30 mph headwind and still have enough fuel to return to its starting point?
Answer provided by our tutors
let
t = 20 hr
v = 150 mph
d = v*t the distance he travels in 20 hours with speed of 150 mph
d = 150*20
d = 3,000 mi
flying with headwind of 30 mph in t1 hours the plane will pass:
(150 - 30)*t1 miles (the speed of the plane is 150 - 30 = 120 mph because of the headwind)
flying back the plane has a tailwind of 30 mph the plane will pass:
(150 + 30)*t2 miles (the speed of the plane is 150 - 30 = 120 mph because of the talewind)
altogether
(150 - 30)*t1 + (150 + 30)*t2 = 3,000
120t1 + 180t2 = 3000 divide both sides by 60
2t1 + 3t2 = 50
we also know that the plane can fly 20 hours:
t1 + t2 = 20
by solving the system of equations:
2t1 + 3t2 = 50
t1 + t2 = 20
we find:
t1 = 10 h
t2 = 10 h
in 10 hours with headwind of 30 mph the plane can travel 120*10 = 1200 mi.