A flight across the US takes longer east to west than it does west to east because of the plane having a headwind flying westward and a tailwind flying eastward. Suppose you are flying from Philadelphia, PA to San Diego, CA. The distance between the cities is 3870 kilometers and the plane's speed in 725 km/r. What is the speed of the wind?

Question

07-04-2018
Mathematics

contestada

A flight across the US takes longer east to west than it does west to east because of the plane having a headwind flying westward and a tailwind flying eastward. Suppose you are flying from Philadelphia, PA to San Diego, CA. The distance between the cities is 3870 kilometers and the plane's speed in 725 km/r. What is the speed of the wind?

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sqdancefan sqdancefan · Answer 1 · 2018-04-07T23:09:30+02:00

sqdancefan sqdancefan

07-04-2018

Let w represent the wind speed.

time = distance/speed

round trip time = time going west + time going east
11 h = (3870 km)/((725 -w) km/h) +(3870 km)/((725 +w) km/h)
11*(725 -w)(725 +w) = 3870*((725 +w) +(725 -w))
11*(725² -w²) = 3870*2*725
11*725²-3880*2*725 = 11*w²
170,375 = 11*w²
124.45 ≈ w

The speed of the wind is approximately 124 km/h.

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