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7. An airplane flies equal distances south-east and then
south-west to finish 120 km due south of its starting-point.
How long is each part of its journey?
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Sagot :

Let's break this problem down step by step.

Let the distance flown south-east be x km.

Let the distance flown south-west be x km (since it flies the same distance in the opposite direction).

The airplane ends up 120 km due south of its starting point, which means that the total distance it has traveled south is 120 km.

      S

      |

      |  x km

      |

      +--------> x km

The total distance traveled south is the hypotenuse of a right triangle with legs of length x and x. Using the Pythagorean theorem, we can write:

x^2 + x^2 = 120^2

2x^2 = 14400

x^2 = 7200

x = √7200 ≈ 84.85 km

So, each part of the journey (flying south-east and then south-west) is approximately 84.85 km.

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