The Pythagorean theorem is sometimes known as Pythagoras' theorem. The speed of the faster person is 40 kmph.
<h3>What is Pythagoras' theorem?</h3>
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
Let the speed of one person be represented by x, then the speed of the other person, if the speed of the second person is 75% of the first.
- Speed of first-person = x
- Speed of second-person = 75% of Speed of first-person = 0.75x
Now, the distance covered by two persons in 2 hours is,
- Distance covered by the first-person = x × 2 = 2x
- Distance covered by the second-person = 0.75x × 2 = 1.5x
Since one person runs towards the south and another towards the east. Therefore, will form a 90° angle between their directions.
Now, the distance between the two after two hours is 100 km, therefore, we can write,
(2x)² + (1.5x)² = 100²
4x² + 2.25x² = 10000
6.25x² = 10000
x² = 10000/6.25
x² = 1600
x = √1600
x = 40
Hence, the speed of the faster person is 40 kmph.
Learn more about Pythagoras' Theorem here:
brainly.com/question/14461977
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