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natali 33 [55]
3 years ago
11

A plane flies 405 miles with the wind and315 miles against the wind in the same amount of time. If the speed of the wind is 20 m

ph find the speed of the plane in still air
Mathematics
1 answer:
gayaneshka [121]3 years ago
4 0

Answer:

  160 mph

Step-by-step explanation:

The relationship between time, speed, and distance is ...

  time = distance/speed

__

If p represents the plane's speed, then the speed with the wind is p+20 and the time to go 405 miles is ...

  405/(p+20)

The speed against the wind is p-20, and the time to go 315 miles is ...

  315/(p-20)

These two times are equal, so we have ...

  405/(p+20) = 315/(p-20)

  405(p-20) = 315(p+20) . . . . . . cross multiply

  90p = 6300 +8100 = 14400 . . . . add 8100 -315p

  p = 14400/90 = 160

The speed of the plane in still air is 160 mph.

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