System of equations

Question

Dave and Sandy Hartranft are frequent flyers with Delta Airlines. They often fly from Philadelphia to Chicago, a distance of 780 miles. On one particular​ trip, they fly into the​ wind, and the flight takes 3 hours. The return​ trip, with the wind behind​ them, only takes 2 hours. If the wind speed is the same on each​ trip, find the speed of the wind and find the speed of the plane in still air.

Answer 1

The distance is the same each way. D = 780

The rate into the wind = (r-w) The time = 3

The rate with the wind = (r + w) The time = 2

Set up a system of linear equations. 3( r-w) = 780

3r -3w = 780

And 2(r + w) = 780

2r + 2w = 780

Solve by multiplying the first equation by 2 and the second by 3 and adding the two equations together to eliminate one variable.

6r - 6w = 2340

6r + 6w = 1560

12r = 3900

r = 325 Substitute the value of r into either equation to find w = 65

The speed of the plane is 365 mph and the speed of the wind is 65 mph.

Answer 2

780 = 3(p - w)

780 = 2(p + w)

Can you solve for p or w and answer?