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

Question

3 years ago

11

ph find the speed of the plane in still air

1 answer:

gayaneshka [121] · Answer 1 · 2022-08-06T10:05:12+03:00

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.