SOLUTION: Another word problem! A six passenger plan cruises at 180 mph in calm air. If the plane flies 7 miles with the wind in the same amount of time as it flies 5 miles against the w

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Another word problem! A six passenger plan cruises at 180 mph in calm air. If the plane flies 7 miles with the wind in the same amount of time as it flies 5 miles against the w      Log On


   

Question 253210: Another word problem!
A six passenger plan cruises at 180 mph in calm air. If the plane flies 7 miles with the wind in the same amount of time as it flies 5 miles against the wind, then what is the wind speed?
Found 3 solutions by drk, Greenfinch, edjones:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
This is a rate x time = distance problem. Here is the table based on the question:
wind . . . . . rate . . . . . . . . . time . . . . . . . . . . .distance
with . . . . . r + 180 . . . . . . . t . . . . . . . . . . . . . . 7
against . . . r - 180 . . . . . . . . t . . . . . . . . . . . . . . 5
The time is distance / rate or
7/(r+180) and 5/(r-180).
Since the times were the same set these fractions equal to each other as:
7/(r+180) = 5/(r-180).
Cross multiply to get
7r - 1260 = 5r + 900
solve for r to get
2r = 2160
r = 1080.
The wind speed is 1080 mph.

Answer by Greenfinch(383) About Me  (Show Source):
You can put this solution on YOUR website!
In a unit of time T
T(180 +w) = 7 and T(180 - w) = 5
so 7/(180 +w) = 5/(180 - w
rearranging 5 x(180 + w) = 7 x(180 - w)
900 + 5x = 1260 - 7w
12w = 360
w = 30

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let w=wind speed, s=speed, d=distance, t=time
s/d=t
(s+w)/7 = (s-w)/5
5(180+w)=7(180-w)
900+5w=1260-7w
12w=360
w=30 mph
.
Ed