SOLUTION: A duck can fly 1800 m in 10 min with the wind. Against the wind, it can fly only 2/3 of this distance in 10 min. How fast can the duck fly in still air? What is the rate of the win

Question 399882: A duck can fly 1800 m in 10 min with the wind. Against the wind, it can fly only 2/3 of this distance in 10 min. How fast can the duck fly in still air? What is the rate of the wind.
**PLEASE USE THE VARIABLES R for rate duck speed in still air and C for rate of wind. IF YOU DO NOT..I WILL GET CONFUSED SINCE I AM USING THOSE AND ONLY THOSE VARIABLES.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
A duck can fly 1800 m in 10 min with the wind. Against the wind, it can fly only 2/3 of this distance in 10 min. How fast can the duck fly in still air? What is the rate of the wind.
**PLEASE USE THE VARIABLES R for rate duck speed in still air and C for rate of wind. IF YOU DO NOT..I WILL GET CONFUSED SINCE I AM USING THOSE AND ONLY THOSE VARIABLES.
..
duck rate = r
wind rate = c
...
with wind, rate = r+c
against wind, rate =r-c
..
distance , with wind = 1800 m
distance,against wind 2/3*1800=1200 m
...
time with wind = 10 minutes====> 1/6 hours
time, against wind =10 minutes====>1/6 hours
...
1800/(r+c)=1/6
cross multiply
r+c=10800......................1
...
1200/(r-c)=1/6
cross multiply
r-c=7200.......................2
...
add (1)&(2)
2r=18000
/2
r=9000 m/minute rate of bird in still air
...
r+c=10,800
9000+c=10,800
c=9,000-8,800
c=1800 m/minute
..
m.ananth@hotmail.ca
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