SOLUTION: Hello - thank you for helping with the following quesiton: With a tail wind, a plane flew 240 km in 45 minutes. With no change in the wind, the return trip took 48 minutes. Fin

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Question 569986: Hello - thank you for helping with the following quesiton:
With a tail wind, a plane flew 240 km in 45 minutes. With no change in the wind, the return trip took 48 minutes. Find the wind speed and the air speed of the plane.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = speed of plane in still air
Let +w+ = wind speed
+s+%2B+w+ = speed of plane with tail wind
+s+-+w+ = speed of plane against the wind
+45+ min = +3%2F4+ hr
+48+ min = +4%2F5+ hr
---------
given:
(1) +s+%2B+w+=+240%2F%28+3%2F4%29+
(2) +s+-+w+=+240%2F%28+4%2F5+%29+
------------------
(1) +s+%2B+w+=+%284%2F3%29%2A240+
(2) +s+-+w+=+%285%2F4%29%2A240+
Add the equations
+2s+=+240%2A%28+4%2F3+%2B+5%2F4+%29+
+s+=+120%2A%28+4%2F3+%2B+5%2F4+%29+
+s+=+120%2A%28+16%2F12+%2B+15%2F12+%29+
+s+=+10%2A%28+16+%2B+15+%29+
+s+=+310+
and
(1) +s+%2B+w+=+%284%2F3%29%2A240+
(1) +310+%2B+w+=+%284%2F3%29%2A240+
(1) +w+=+320+-+310+
(1) +w+=+10+
Air speed is 310 km/hr
wind speed is 10 km/hr
check:
(1) +s+%2B+w+=+240%2F%28+3%2F4%29+
(1) +310+%2B+10+=+240%2F%28+3%2F4%29+
(1) +320+=+%284%2F3%29%2A240+
(1) +960+=+4%2A240+
(1) +960+=+960+
and
(2) +s+-+w+=+240%2F%28+4%2F5+%29+
(2) +310+-+10+=+240%2F%28+4%2F5+%29+
(2) +300+=+%285%2F4%29%2A240+
(2) +1200+=+1200+
OK