SOLUTION: A plane has a speed of p km/hr in still air. It makes a round trip, flying with and against a wind of w km/hr. Show that its average speed is (p^2 -w^2)/p km/hr.

Algebra ->  Finance -> SOLUTION: A plane has a speed of p km/hr in still air. It makes a round trip, flying with and against a wind of w km/hr. Show that its average speed is (p^2 -w^2)/p km/hr.      Log On


   

Question 886066: A plane has a speed of p km/hr in still air. It makes a round trip, flying with and against a wind of w km/hr. Show that its average speed is (p^2 -w^2)/p km/hr.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
d = each one-way distance for the round trip.

G = time going, and R = time returning.

choose against wind going and with wind returning.
%28p-w%29G=d and %28p%2Bw%29R=d
G=d%2F%28p-w%29 and R=d%2F%28p%2Bw%29

Average speed is distance of whole round trip DIVIDED by time of whole round trip.
Distance was 2d.
Total time was G%2BR=d%2F%28p-w%29%2Bd%2F%28p%2Bw%29.

Average Speed, %282d%29%2F%28d%2F%28p-w%29%2Bd%2F%28p%2Bw%29%29

2%2F%281%2F%28p-w%29%2B1%2F%28p%2Bw%29%29

2%2F%28%28p%2Bw%29%2B%28p-w%29%29%2F%28p%5E2-w%5E2%29

2%28p%5E2-w%5E2%29%2F%28p%2Bw%2Bp-w%29

2%28p%5E2-w%5E2%29%2F%282p%29

cross%282%29%28p%5E2-w%5E2%29%2F%28cross%282%29p%29-----THERE!