Answer
$5$ seconds and $7.5$ seconds
Work Step by Step
The equation for distance at any time is $$d = | 300 - 48t |.\tag{1}$$ To get the time when $d$ was equal to $60$, we substitute $d=60$ in equation $(1)$: $$60 = | 300 - 48t |.\tag{2}$$ We solve equation $(2)$.
a) Equate $$300 - 48t = 60.$$ Subtract $300$ from both sides $$-48t = -240.$$ Divide both sides by $-48$ $$t = 5.$$
b) Equate $$300 - 48t = -60.$$ Subtract $300$ from both sides $$-48t = -360.$$ Divide both sides by $-48$ $$t = 7.5.$$ The times when the car is $60$ ft away from us will be $5$ seconds and $7.5$ seconds.
