SOLUTION: An executive flew in the corporate jet to a meeting in a city 1500 kilometers away. After traveling the same amount of time on the return flight, the pilot mentioned that they stil
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Question 1019370: An executive flew in the corporate jet to a meeting in a city 1500 kilometers away. After traveling the same amount of time on the return flight, the pilot mentioned that they still had 300 kilometers to go. The air speed of the plane was 600 kilometers per hour. How fast was the wind blowing? (Assume that the wind direction was parallel to the flight path and constant all day. Round your answer to two decimal places.) Found 2 solutions by robertb, josmiceli:Answer by robertb(5830) (Show Source):
You can put this solution on YOUR website! Let r = wind speed.
In the outbound flight of the plane, its net speed will be 600 + r, while in the return trip it would be 600 - r. (The plane would be flying parallel AGAINST the wind.)
In the outbound flight, using the formula d = r*t, the time duration of flight is hours.
In the return flight, after travelling hours, the plane has traveled kilometers. And there is still 300 kilometers to go. Thus
==>
==>
Cross-multiplying, we get
2400+4r = 3000 - 5r
==> 9r = 600 ==> r = 66.67 kilometers per hour.
You can put this solution on YOUR website! On the return flight, the plane flew for the same
amount of time, but went a shorter distance.
That means the wind was blowing against the
plane on the return flight and with the plane
going to the meeting
----------------------
Let = the wind speed
Let = the speed of the plane in still air
Let = the flight to the meeting and the
flight km short of returning
--------------------------------- km is the distance
of the return flight km/hr km/hr
-----------------------
Equation for the flight to the meeting:
(1)
Equation for km of the return flight:
(2)
------------------------
By substitution:
(1)
(2)
--------------------
(2) hrs
and
(1)
(1)
(1)
(1)
(1)
The windspeed is 75 km/hr
-----------------------
check:
(1)
(1)
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
(2)
OK
