### Home > CC4 > Chapter 10 > Lesson 10.1.3 > Problem10-59

10-59.

An airplane flying into the wind travels $1809$ miles between two cities in $3$ hours and $36$ minutes. On the return flight, the same distance is traveled in $3$ hours. Find the ground speed of the plane and the speed of the wind in miles per hour, assuming both remain constant. (Ground speed is the speed of the plane if there were no wind.) Homework Help ✎

Distance traveled $=$ Rate $×$ Time
Set up a system of equations to model this problem.

Let $r$ represent the rate (ground speed) of the plane, and $x$ represent the speed of the wind.

Against the wind: $1809 = (r − x) × 3.6$
With the wind: $1809 = (r + x) × 3$