Question

Another friend's distance d from you (in feet) after t seconds is given by
d = |80 - 5t|. What does the 80 in the equation represent? What does the 5 in the equation represent? At what times is she 60 ft from you?
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Answer 1

I think the 80 represents how far away they initially start from you

And the 5 is their speed

d=|80-5t|
60=|80-5t| |square both sides
60² = (80-5t)(80-5t)
3600 = 6400-400t-400t +25²
25t²-800t +6400 =3600
25t² -800t + 2800=0
5t² -160t +560=0
(ax²+bx+c=0)
(a=+5 b=-160 c=+560)
Sub into -b formula
x=(-b±√(b²-4ac))/(2a)
t= (-(-160)±√((-160)²-4(5)(560))/(2(5)) .


Should get t=4 seconds and t=28 seconds
sub both values back in to make sure

d=|80-5(4)|
d=|80-20|
d=60ft

d=|80-5(28)|
d=|80-140||
d=60ft