Question

An airplane flying into a headwind travels 1800 miles in 3 hours and 36 minutes. On the return flight, the same distance is traveled in 3 hours. Find the speed of the plane in still air and the speed of the wind, adding both remain constant throughout the trip.

Please show detailed work!!

Answer 1

Answer: speed of the plane in still air = 550 miles per hour

the speed of the wind = 50 miles per hour

Explanation:

The airplane travelled 1800 miles in 3 hours and 36 minutes while flying into a headwind travels 1800 miles

Converting 36 minutes to hours, it becomes

36/60 = 0.6 hours.

The time becomes 3 + 0.6 = 3.6 hours

So the airplane travelled 1800 miles in 3.6 hours while flying into a headwind travels 1800 miles

Speed = distance / time

So the speed of the airplane while flying into the head wind = 1800/3.6 = 500 miles per hour

On returning, the same distance is traveled in 3 hours.

Speed on returning

= 1800/3 = 600 miles per hour

Let x = the speed of the airplane in still air

Let y = the speed of the wind

While flying into the headwind,

x - y = 500 - - - - - -1

while returning,

x +y = 600 - - - - - - 2

Subtracting equation 2 from equation 1,

-y - y = 500 - 600

-2y = - 100

y = -100/-2 = 50 miles per hour

x = 600 - y = 600 - 50

x = 550 miles per hour