SOLUTION: This is a word problem I am having trouble setting it up. It takes 5 hours for a jet plane traveling from L.A to New York with a wind blowing it from west to east. On the return

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Question 796955: This is a word problem I am having trouble setting it up.
It takes 5 hours for a jet plane traveling from L.A to New York with a wind blowing it from west to east. On the return trip it took the jet plane 6 hours. The distance between L.A and New York is approximately 4,000 miles.
How fast is the airplane if there is no wind? And how fast was the wind blowing?
Found 3 solutions by solver91311, josmiceli, richwmiller:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


5 hours to go 4000 miles is 800 miles per hour: Still air speed PLUS wind speed

6 hours to go 4000 miles is 666 2/3 miles per hour: Still air speed MINUS wind speed.





Solve the 2X2 system.

John

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My calculator said it, I believe it, that settles it
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +w+ = the speed of the wind
Let +s+ = the speed of the plane in still air
+s+%2B+w+ = the plane's speed going LA to NY
+s+-+w+ = the plane's speed going NY to LA
----------------
Flying LA to NY:
(1) +4000+=+%28+s+%2B+w+%29%2A5+
Flying NY to LA:
(2) +4000++=+%28+s+-+w+%29%2A6+
-----------------------
(1) +4000+=+5s+%2B+5w+
(2) +4000+=+6s+-+6w+
---------------------
Multiply both sides of (1) by +6+
Multiply both sides of (2) by +5+
Then add the equations
---------------------
(1) +24000+=+30s+%2B+30w+
(2) +20000+=+30s+-+30w+
+44000+=+60s+
+s+=+733.333+
and
(1) +4000+=+5s+%2B+5w+
(1) +800+=+s+%2B+w+
(1) +w+=+800+-+733.333+
(1) +w+=+66.666+
The speed of the wind is 66.666 mi/hr
The speed of the plane in still air is 733.333 mi/hr
-----------
check:
(1) +4000+=+%28+s+%2B+w+%29%2A5+
(1) +4000+=+%28+733.333+%2B+66.666+%29%2A5+
(1) +4000+=+800%2A5+
(1) +4000+=+4000+
and
(2) +4000++=+%28+s+-+w+%29%2A6+
(2) +4000++=+%28+733.333+-+66.666+%29%2A6+
(2) +4000+=+666.666%2A6+
(2) +4000+=+4000+
OK


Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Distance from la to nyc is 2464 miles