A commercial jetliner with an air speed of 640 mi/hr leaves Chicago and flies due west at the same time that a small single-engine plane with an air speed of 180 mi/hr leaves Chicago and flies due east. Determine the speed of a wind blowing from the west if the jetliner is 1500 mi west of Chicago when the single-engine plane is 550 mi east of Chicago.

  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

__

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.

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.

h/o/e/s mad

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