with a tail wind a helicopter traveled 300mi in an hour and

with a tail wind, a helicopter traveled 300mi in an hour and 40 min. the return trip aganst the same wind took 20 min longer. find the wind speed and also the air speed of the helicopter

Solution

The formula to use is: Distance = rate x time or d = rt
The distance traveled was 300 mi. The rate on the first trip {WITH tail wind} is h {helicopter} + w {wind}. The time is 1 hour and 40 minutes, or 1.67 hours
So, you have 300 = (h + w)1.67
The rate on the second trip {AGAINST wind} is {h - w}, and an additional 20 minutes, so 2 hours. So you have 300 ={h - w)2
Solve for h in the second trip:
300 = 2(h-w)
300 = 2h - 2w
Add the 2w to both sides to isolate the 2h
300 + 2w = 2h
Divide both sides by 2 to isolate the h
150 + w = h OR h = 150 + w
Now, plug that info into Trip 1:
300 = 1.67(h+w) OR 300 = 1.67 ([150 + h) + w)
300 = 250.5 + 1.67w + 1.67w
300 = 250.5 + 3.34w
Subtract the 250.5 from both sides to isolate the 3.34w
49.5 = 3.34w
Divide both sides by 3.34 to isolate the w
14.8 = w.... round up to w = 15 Wind speed is 15
Plug that into the formula:
300 = (h + 15)1.67
300 = 1.67h + 25.05
Subtract 25.05 from 300 to isolate the 1.67h
274.75 = 1.67h
164.6 = h
Round up to 165 is Air Speed.
So... Wind speed is 15; Air speed is 165.