Answer :
The equation that represents the distance, d, between the friends after t hours is d = √(3250t²)
Calculating distance
From the question, we are to write an equation for the distance between the friends after t hours
From the given information,
"One heads North at 45 miles per hour, while the other heads East at 35 miles per hour"
First, we will calculate the distance each of them has traveled after t hours
Using the formula,
Distance = Speed × Time
Distance covered by the friend that heads North is
Distance = 45 × t
Distance = 45t
Distance covered by the friend that heads East is
Distance = 35 × t
Distance = 35t
Now, for the distance, d, between the two friends after t hours
Using the Pythagorean theorem, we can write that
d² = (45t)² + (35t)²
d² = 2025t² + 1225t²
d² = 3250t²
d = √(3250t²)
Hence, the equation that represents the distance, d, between the friends after t hours is d = √(3250t²)
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