|
Question 173418: A six-passenger plane 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?
I have no idea how to start this question. I tried D=RT but i got no where
Found 2 solutions by stanbon, gonzo:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A six-passenger plane 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?
--------------------------------------------
Yes, use d= rt
------------------
With-wind DATA:
distance = 7 miles; rate = 180+wind ; time = d/r = 7/(180+w) hrs
--------------
Against-wind DATA:
distance = 5 miles ; rate = 180-w ; time = d/r = 5/(180-w) hrs
-------------
time = time
7/(180+w) = 5/(180-w)
7(180-w) = 5(180+w)
7*180 - 7w= 5*180 + 5w
12w = 2*180
w = 2*15
wind speed = 30 mph
=======================
Cheers,
Stan H.
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website! d = rt is a good place to start.
r = 180 mph for the plane in calm air.
r = 180 + w is for when the plane flies with the wind.
r = 180 - w is for when the plane flies against the wind.
-----
t equals time
d equals distance
-----
since time is the same whether the plane flies with the wind or against it, then the same variable t applies for both.
-----
with the wind, the equation:
d = r*t
becomes:
7 = (180+w) * t
-----
against the wind, the equation:
d = r*t
becomes:
5 = (180-w) * t
-----
solve for t in both equations:
with the wind:
t = 7 / (180+w)
against the wind:
t = 5 / (180-w)
-----
since both equations equal to t, then they are equal to each other:
7 / (180+w) = 5 / (180-w)
-----
multiply both sides by (180+w)*(180-w) and you get:
7*(180-w) = 5*(180+w)
simplify each side of the equation to get:
1260 - 7*w = 900 + 5*w
add 7*w to both sides of the equation to get:
1260 = 900 + 12*w
subtract 900 from both sides of the equation to get:
360 = 12*w
divide both sides of the equation by 12 to get:
w = 30
-----
since w = 30, then:
with the wind equation becomes:
7 / (180+30) = t
simplify:
7 / 210 = t
t = 1/30
-----
since t = 1/30, and w = 30, then against the wind equation becomes:
5 / (180-30) = 1/30
simplify to get:
5 / 150 = 1/30
1 / 30 = 1/30
-----
both equations check out.
wind speed = 30 mph.
amount of time was 1/30 hours = 2 minutes
-----
|
|
|
| |
