Question 937943: Please help me solve this word problem:
Traveling with the wind, a plane takes 2 1/2 hours to fly a distance of 1500 miles. The return flight against the wind takes 3 hours. Find the speed of the plane and the speed of the wind.
Thank you for reading and please help me as soon as possible.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Traveling with the wind, a plane takes 2 1/2 hours to fly a distance of 1500 miles.
The return flight against the wind takes 3 hours.
Find the speed of the plane and the speed of the wind.
:
let s = speed of the plane
let w = speed of the wind
then
(s+w) = the effective speed with the wind
and
(s-w) = effective speed against the wind
:
Write a distance equation for each way; dist = time * speed
2.5(s+w) = 1500
3(s-w) = 1500
Simplify both equations, divide the 1st by 2.5 and the 2nd by 3, resulting in:
s + w = 600
s - w = 500
---------------Adding eliminates w, find s
2s = 1100
s = 1100/2
s = 550 mph speed of the plane
Find w
550 + w = 600
w = 600 - 550
w = 50 mph is the speed of the wind
:
:
Check this using the original 2nd equation
3(550 - 50) = 1500
3(500) = 1500
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