Problem: A plane flew straight against a wind between two towns in 84 minutes and returned with that wind in 9 minutes less than it would take in still air. The number of minutes (2 answers) for the return trip was
Answer Choices:
A. 54 or 18
B. 60 or 15
C. 63 or 12
D. 72 or 36
E. 75 or 20
Solution:
Let d,v,w, denote the distance between the towns, speed against, speed with the wind respectively. Then since d/v=84,d=84v, we have
wd​=21​(w+v)d​−9 or 84wv​=21​(w+v)84v​−9.
Letting x=v/w, the last equation reduces to 28x=x1​+156​−3 which is equivalent to 28x2−25x+3=0. (4x−3)(7x−1)=0,x=43​ or 71​.
The number of minutes required for distance d at speed w with the wind is
wd​=84 wv​=84 43​ or 8471​=63 or 12 minutes.