SOLUTION: Please help me solve this question: In 2hours 30 minutes an airplane travels 600 km against the wind. The return trip (with the wind) takes 1 hour 40 minutes. Find the speed of the

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Question 920756: Please help me solve this question: In 2hours 30 minutes an airplane travels 600 km against the wind. The return trip (with the wind) takes 1 hour 40 minutes. Find the speed of the wind and the speed of the airplane in still air.
I used D=RT plugging in 600 and 150 (2hr30min) and the answers aren't matching up with the answers on the sheet.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
In 2hours 30 minutes an airplane travels 600 km against the wind.
The return trip (with the wind) takes 1 hour 40 minutes.
Find the speed of the wind and the speed of the airplane in still air.
:
Since we are dealing in km/hr, Convert the given times to hrs
2 hr 30 min = 2.5 hrs
1 hr 40 min = 1 hrs (40/60)
:
let s = speed in still air
let w = speed of the wind
then
(s+c) = speed with the wind
and
(s-c) = speed against the wind
:
Write a distance equation for each way
2.5(s - c) = 600
1(s + c) = 600
we can greatly simplify these equations, divide the 1st by 2.5 the 2nd by 1 and we have
s - c = 240
s + c = 360
--------------adding eliminates c, find s
2s = 600
s = 300 km/hr in still air
find w
300 + c = 360
c = 60 km/hr is the speed of the wind
:
Check these solutions in the original equations