Question 134375: when a plane flies into the wind, it can travl 3000 km in 6 hours. when it flies with the wind, it can travel the same distance in 5 hours. Find the rate of the plane in still air and the rate of the wind.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! when a plane flies into the wind, it can travel 3000 km in 6 hours. when it flies with the wind, it can travel the same distance in 5 hours. Find the rate of the plane in still air and the rate of the wind.
:
Let s = speed of plane in still air
let w = speed of the wind
then
(s-w) = ground speed into the wind
and
(s+w) = ground speed with the wind
:
Write 2 distance equations: Dist = time * speed:
6(s-w) = 3000
5(s+w) = 3000
:
Simplify both equations; divide the 1st one by 6; the 2nd one by 5, you have:
s - w = 500
s + w = 600
--------------adding equations eliminates w, find s:
2s +0 = 1100
s = 1100/2
s = 550 km/hr plane speed in still air
:
Find w using s + w = 600
550 + w = 600
w = 600-550
w = 50 km/hr is the speed of the wind
:
:
Check solutions in the 1st original equation
6(550 - 50) = 3000; confirms our solution
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