SOLUTION: A duck can fly 2400 m in 10 minutes with the wind. Against the wind, it can fly only 2/3 of this distance in 10 minutes. What is the rate of the wind?

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Question 242866: A duck can fly 2400 m in 10 minutes with the wind. Against the wind, it can fly only 2/3 of this distance in 10 minutes. What is the rate of the wind?

Found 2 solutions by checkley77, JimboP1977:
Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website!
2,400/10=240 m/m.
2/3*2,400/10=2*800/10=1,600/10=160 m/m.
(240-160)/2=80/2=40 m/m is the speed of the wind.
Proof:
240-40=200 m/m. is the speed of the duck.
160+40=200 ditto.

Answer by JimboP1977(311) (Show Source):
You can put this solution on YOUR website!
Well we know that distance/time = speed.
So the duck's OWN speed (if flying without any wind) with the wind behind him is:
Where x/10 is the wind speed
The duck's OWN speed (if flying without any wind) with the wind against him is:
Where x/10 is the wind speed Remember
So we have two equations that must equal each other since they both represent the duck's speed.
We need to rearrange to find x
Add x/10 to both sides and subtract (1600/10 from both sides gives:

so x must be 400/10 which 40 metres per minute.