SOLUTION: An airplane encountered a head wind during a flight between Joppetown and Jawsburgh which took 4 hours and 36 minutes. The return flight took 4 hours. If the distance from Joppet

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Question 1094426: An airplane encountered a head wind during a flight between Joppetown and Jawsburgh which took 4 hours and 36 minutes. The return flight took 4 hours. If the distance from Joppetown to Jawsburgh is 1400 ​miles, find the airspeed of the plane​ (the speed of the plane in still​ air) and the speed of the​ wind, assuming both remain constant.
Found 3 solutions by josmiceli, addingup, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the plane in still air
Let +w+ = the wind speed
+36%2F60+=+.6+ ( minutes to hrs )
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Flying against the wind:
(1) +1400+=+%28+s+-+w+%29%2A4.6+
Flying with the wind:
(2) +1400+=+%28+s+%2B+w+%29%2A4+
---------------------------
(2) +1400+=+4s+%2B+4w+
(2) +4s+=+1400+-+4w+
(2) +s+=+350+-+w+
---------------------------
Plug (2) into (1)
(1) +1400+=+%28+350+-+w+-+w+%29%2A4.6+
(1) +1400+=+%28+350+-+2w+%29%2A4.6+
(1) +1400+=+1610+-+9.2w+
(1) +9.2w+=+1610+-+1400+
(1) +9.2w+=+210+
(1) +w+=+22.826+
and
(2) +s+=+350+-+22.826+
(2) +s+=+327.174+
---------------------------
The speed of the plane in still air is 327.174 mi/hr
The wind speed is 22.826 mi/hr
-------------------------------
check:
(1) +1400+=+%28+s-w+%29%2A4.6+
(1) +1400+=+%28+327.174+-+22.826+%29%2A4.6+
(1) +1400+=+304.348%2A4.6+
(1) +1400+=+1400.0008+
close enough
(2) +1400+=+%28+s%2Bw+%29%2A4+
(2) +1400+=+%28+327.174+%2B+22.826+%29%2A4+
(2) +1400+=+350%2A4+
(2) +1400+=+1400+
OK
Get a 2nd opinion if needed

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
distance/time = rate
----------------------------------
1400/(240 + x) = 1400/276 <---hours to minutes
(x+240)/1400 = 69/350
x + 240 = 69/350 * 1400/1
x + 240 = 276
x = 36
36/2 = 18
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1400/240+18 = 5.43; 1400/276-18 = 5.43 Correct

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
An airplane encountered a head wind during a flight between Joppetown and Jawsburgh which took 4 hours and 36 minutes. The return flight took 4 hours. If the distance from Joppetown to Jawsburgh is 1400 ​miles, find the airspeed of the plane​ (the speed of the plane in still​ air) and the speed of the​ wind, assuming both remain constant.
Correct answers: