Two friends drive off in different directions from the same place. One heads North at 40 miles per hour, while the other heads E

Question

yaroslaw [1]

1 year ago

8

Two friends drive off in different directions from the same place. One heads North at 40 miles per hour, while the other heads E

ast at 20 miles per hour. Complete an equation for the distance between the friends after t hours.

Mathematics

1 answer:

Natalka [10] · Answer 1 · 2024-09-24T13:02:39+03:00

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