need help in math

Question

A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hour 12 minutes. What is his speed in still air, and how fast is the wind blowing?

Answer 1

12 minutes = 12/60 part of an hour = 1/5

1 hour and 1/5 = 6/5 hr.

distance = time times speed

d=rt

180 = 2(p -w) where w = wind speed and p=plane speed in still air

90 = p-w

180= (6/5)(p+w)

30 = (p+w)/5

150 = p+w

p+w=150

p-w= 90

add to eliminate one variable

2p = 240

divide by 2

p = 120 mph = plane speed in still air

w = 150-120 = 30 mph = wind speed

check the answers:

2 hours at 120-30 or 90 mph is

2(90) = 180 miles

1 hr 15 minutes = 6/5 hr at 120+30=150 mph is

(6/5)150= 6(30) = 180 miles