Applications and Functions

Question

Rajib flies a small plane a distance of 2000 miles. Because he is flying into a headwind, the trip takes 10 hours. On the way back, the wind is still blowing in the same direction with the same wind speed, so it only takes 8 hours. What is the speed of the plane in still air, and how fast is the wind blowing?

Answer 1

Hi Genesis,

Speed=distance/time---------->distance=speed*time. And the distance is constant. We can decompose this problem into two parts: going and returning

Let w=wind p=plane speed

Going: 2000=(p-w)(10)--------->p-w=200 (1)

Returning: 2000=(p+w)(8)-------->p+w=250 (2)

Solve by any method (elimination is quickest here because you just add (1) and (2) and are left with one variable)

2p=450 ----------->p=225 mph

plug into either equation w=250-225= 25mph