SOLUTION: A certain plane flying with the wind travels 540 km in 2 hours. Later, flying against the same wind, the plane travels 690 km in 3 hours. Find the speed of the plane in still air a

Question 205013: A certain plane flying with the wind travels 540 km in 2 hours. Later, flying against the same wind, the plane travels 690 km in 3 hours. Find the speed of the plane in still air and the speed of the boat.
A boat takes 3 hours to go 24 km upstream. It can go 36 km downstream in the same time. Find the speed of the current and the speed of the boat.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A certain plane flying with the wind travels 540 km in 2 hours.
Later, flying against the same wind, the plane travels 690 km in 3 hours.
Find the speed of the plane in still air, and the speed of the wind.
:
let s = plane speed in still air
let w = speed of the wind
then
(s+w) = effective speed with the wind
(s-w) = effective speed against
:
Write two distance equations: dist = time * speed
2(s + w) = 540; (with the wind)
3(s - w) = 690; (against the wind}
:
We can simplify both these equations, divide the 1st by 2 and the 2nd by 3:
s + w = 270
s - w = 230
--------------addition eliminates w, find s
2s = 500
s = 250 km/hr speed in still air
:
Find the speed of the wind:
250 + w = 270
w = 270 - 250
w = 20 km/hr speed of the wind
:
:
A boat takes 3 hours to go 24 km upstream.
It can go 36 km downstream in the same time.
Find the speed of the current and the speed of the boat.
:
Do this problem exactly the same way:
3(s - c) = 24
3(s + c) = 36
:
Let me know if you need help.
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