Answer
t = 4.444 seconds or t = 17.77 seconds
Work Step by Step
$abs (200 - 18t) = d$
We want a distance of 120 feet (and also -120 feet, as my friend would still be deemed 120 feet away from me).
$200 - 18t = 120$
$200 - 18t - 120 + 18t = 120 - 120 + 18t$
$80 = 18t $
$80/18 = 18t/18$
$4.444 = t $
$200 - 18t = -120$
$200 - 18t +120 +18t = -120 +120 + 18t$
$320 = 18t$
$320/18 = 18t/18$
$17.77 = t $