SOLUTION: An airplane can travel 450 miles into the wind in 2 hours and 25 minutes. This plane takes the same time to travel 630 miles with the wind. Find the speed of the airplane without a

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: An airplane can travel 450 miles into the wind in 2 hours and 25 minutes. This plane takes the same time to travel 630 miles with the wind. Find the speed of the airplane without a      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 329025: An airplane can travel 450 miles into the wind in 2 hours and 25 minutes. This plane takes the same time to travel 630 miles with the wind. Find the speed of the airplane without any wind.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let w = wind speed
Let a = speed of plane without wind
a+-+w = speed of plane flying into wind
a+%2B+w = speed of plane flying with the wind
given:
450+=+%28a+-+w%29%2A2.4167
630+=+%28a+%2B+w%29%2A2.4167
This is 2 equations with 2 unknowns so it's solvable
-------------------
Divide both sides of each by 2.4167
a+-+w+=+450%2F2.4167
a+%2B+w+=+630%2F2.4167 add the equations
-------------------
2a+=+1080%2F2.4167
2a+=+446.890
a+=+223.4452 mi/hr
and, since
a+%2B+w+=+630%2F2.4167
w+=+260.686+-+223.4452
w+=+37.241 mi/hr
The speed of the plane without wind is 223.445 mi/hr
check:
450+=+%28a+-+w%29%2A2.4167
450+=+%28223.4452+-+37.241%29%2A2.4167
450+=+186.2042%2A2.4167
450+=+449.9997 close enough
and
630+=+%28a+%2B+w%29%2A2.4167
630+=+%28223.4452+%2B+37.241%29%2A2.4167
630+=+260.6862%2A2.4167
630+=+630.0003
OK