question in lower description

Question

A plane flies 405 miles with the wind and 315 miles against the wind in the same length of time. If the speed of the wind is 20 mph, find the speed of the plane in still air.

Answer 1

distance = rate x time

 

405 = (r + 20) x time

 

315 = (r - 20) x time

 

Solves each for time and sets them equal

 

405/(r+20) = 315/(r-20)

 

Cross multiplies:

 

405(r-20) = 315(r+20)

 

405r - 8100 = 315r + 6300

 

405r - 315r = 6300 + 8100

 

90 r = 14400

 

9 r = 1440

 

r = 160

 

The speed of the plane is 160 miles per hour.

 

With the wind, it flies 180 miles per hour. The time it takes to fly that distance is 405/180 = 2.25 hours or

                                                                                                                                2 hours and 15 minutes.

 

Against the wind, it flies 140 miles per hour. It takes 315/140 = 2.25 hours, the same amount of time.

This proves the answer is correct.

 

The speed of the plane is 160 mph.