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# help

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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.

Feb 14, 2020

### 1+0 Answers

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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)

Feb 14, 2020