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.
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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.
Let the wind speed = W
Note that if the wind is blowing from the west, its direction is toward the east
So....the wind slows the regular rate of the large plane flying west and increases the regular rate of the small plane flying east
Here's a ( bad) pic of the situation
640 - W < Chicago > 180 + W
Note that Distance / Rate = Time
But.....they fly the same time....so...
Distance the large plane has flown Distance the small plane has flown
____________________________ = _______________________________
Effective rate Effective rate
1500 550
_______ = _______ cross-multiply
640 - W 180 + W
1500 ( 180 + W) = 550 ( 640 - W) simplify
270000 + 1500 W = 352000 - 550W add 550W to both sides, subtract 270000 from both sides
2050W = 82000 divide both sides by 2050
W = 40 (mi /hr)
