SOLUTION: a small plane traveled the 1800 km distance between two islands in 3 hours with the wind. the return trip against the wind took 6 hours . find the rate of the plane in still air an

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Question 703980: a small plane traveled the 1800 km distance between two islands in 3 hours with the wind. the return trip against the wind took 6 hours . find the rate of the plane in still air and the rate of the wind
Found 3 solutions by Alan3354, lwsshak3, vidya pattar:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
a small plane traveled the 1800 km distance between two islands in 3 hours with the wind. the return trip against the wind took 6 hours . find the rate of the plane in still air and the rate of the wind
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Find the 2 groundspeeds using r = d/t
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The plane's airspeed is the average of the 2.
The windspeed is the difference between airspeed and groundspeed.
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"the rate of the plane in still air" is a moronic statement.

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
a small plane traveled the 1800 km distance between two islands in 3 hours with the wind. the return trip against the wind took 6 hours . find the rate of the plane in still air and the rate of the wind.
..
let x=rate of airplane in still air
let c=rate of wind
x+c=rate of airplane downwind
x-c=rate of airplane upwind
travel time=distance/rate
1800/(x+c)=3
1800/(x-c)=6
..
3x+3c=1800
6x-6c=1800
..
6x+6c=3600
6x-6c=1800
12x=5400
x=450
rate of airplane in still air=450 km/hr

Answer by vidya pattar(14) About Me  (Show Source):
You can put this solution on YOUR website!
Solution:
Let assume that the rate of the plane in still air is x km/hr
and the rate of the wind is y km/hr
now since plane travels 1800 km with the wind , it means
speed = distance / time taken,
total distance = 1800 / 3
x + y = 600
now while return trip the plane travels against the wind and take 6 hrs ,
hence speed = x - y = 1800 / 6
x - y = 300
now solve the system of equation obtained above:
x + y = 600
x - y = 300
hence by adding both the equation we get :
2x = 900
x = 450
now to find the rate of the wind is = x + y = 600
450 + y = 600
y = 600 - 450
y = 150
hence speed of the plane in still air is 450 m / hr
and speed of the wind is 150 km/hr .
Thanks
Best regards .