Answer:
40 mph
Step-by-step explanation:
The speed of separation of the two airplanes traveling in opposite directions is the sum of their respective airspeeds:
640 mi/h + 180 mi/h = 820 mi/h
At the time of interest, their separation distance is ...
1500 mi + 550 mi = 2050 mi
Then the time it took to achieve that separation was ...
time = distance/speed = (2050 mi)/(820 mi/h) = 2.5 h
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The actual ground speed of the jetliner was ...
speed = distance/time = 1500 mi/(2.5 h) = 600 mi/h
Since the airspeed of the jet is 640 mi/h, the speed of the air must have subtracted 40 mi/h from its headway.
The wind from the west is 40 mi/h.
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Check
The wind adds to the speed of the small plane, so its ground speed is ...
180 mph +40 mph = 220 mph
and the distance it travels in 2.5 hours is ...
distance = speed × time = (220 mi/h)(2.5 h) = 550 mi
This value matches the problem statement, so the answer checks OK.
