Question

Use two equations in two variables to solve the problem.

An airplane can fly with the wind a distance of 800 miles in 8 hours. However, the return trip against the wind takes 10 hours. Find the speed of the plane in still air and the speed of the wind.

Answer 1

p = plane's speed in calm air

w = wind's speed

p + w = speed across the ground of the plane flying with the wind

p - w = speed across the ground of the plane flying against the wind

NOTE : distance = speed × time

distance = 800 miles

800 = 8(p+w) :: given that it takes 8 hrs with the wind to travel 800 miles

800 = 10(p-w) :: given that it takes 10 hrs against the wind to travel 800 miles

so we have

8(p+w) = 800

10(p-w) = 800

.

8p + 8w = 800 ---------------- ( 1 )

10p - 10w = 800 ------------------ ( 2 )

Multiplying the first equation with 10 and the second with 8

80p + 80w = 8000

80p - 80w = 6400

.

160p = 14400

p = 14400 / 160

p = 90 ( this is the plane's speed )

Substitute this into any equation

( 80 ) ( 90 ) + 80w = 8000

7200 + 80w = 8000

80w = 800

w = 10

Wind speed = 10 miles per hours

plane speed = 90 miles per hour

Hope my answer helps!