An equation for the distance between the friends after time (t) in hours is c = 4t√125.
<h3>How to determine an equation for the distance between the friends?</h3>
In order to determine an equation for the distance between the friends after an amount of time (t) in hours, we would create a mental image of a right-angled triangle because they both head in the opposite (North) and adjacent (East) direction.
Therefore, the distance between them after t hours represent the hypotenuse of a right-angled triangle, which can be calculated by using Pythagorean theorem.
Next, we would determine the distance covered by each friend:
For the first friend (North), we have:
Distance, a = speed × time
Distance, a = 40t
For the second friend (East), we have:
Distance, b = speed × time
Distance, b = 20t
By applying Pythagorean theorem, the distance between the friends after an amount of time (t) is given by:
Distance, c² = a² + b²
Distance, c² = (40t)² + (20t)²
Distance, c² = 1600t² + 400t²
Distance, c² = 2000t²
Distance, c = √(16 × 125t²)
Distance, c = √16t² × √125
Distance, c = 4t√125
<u>Note:</u> The prime factorization of 2000 is 2⁴ × 5³ = 16 × 125.
Read more on distance here: brainly.com/question/28606453
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