Question

Two friends drive off in different directions from the same place. One heads North at 40 miles per hour, while the other heads East at 20 miles per hour. Complete an equation for the distance between the friends after t hours.

Answer 1

An equation for the distance between the friends after time (t) in hours is c = 4t√125.

How to determine an equation for the distance between the friends?

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

Note: The prime factorization of 2000 is 2⁴ × 5³ = 16 × 125.

Read more on distance here: brainly.com/question/28606453

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