SOLUTION: A plane traveled 400 miles to Rome and back. The trip there was with the wind. It took 4 hours. The trip back was into the wind. The trip back took 8 hours. Find the speed of the p

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Question 644508: A plane traveled 400 miles to Rome and back. The trip there was with the wind. It took 4 hours. The trip back was into the wind. The trip back took 8 hours. Find the speed of the plane in still air and the speed of the wind.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let speed of plane in still air = +p+
Let the wind speed = +w+
given:
Equation with the wind
(1) +400+=+%28+p+%2B+w+%29%2A4+
Equation against the wind
(2) +400+=+%28+p+-+w+%29%2A8+
--------------------
Multiply both sides of (1)
by +2+ and
Add the equations
(1) +800+=+8p+%2B+8w+
(2) +400+=+8p+-+8w+
+1200+=+16p+
+p+=+75+
Plug this result back into (1) or (2)
(1) +400+=+%28+75+%2B+w+%29%2A4+
(1) +400+=+300+%2B+4w+
(1) +4w+=+100+
(1) +w+=+25+
The speed of the plane in still air is 75 mi/hr
The wind speed is 25 mi/hr
check:
(2) +400+=+%28+75+-+25+%29%2A8+
(2) +400+=+50%2A8+
(2) +400+=+400+
OK