Answer:
1 hour
Explanation:
Since the definition of velocity is [tex]v=x/t[/tex], we can calculate the position at time t of an object moving at speed v with [tex]x=vt[/tex].
The position of the first ferry is [tex]x_1=v_1t[/tex]
The position of the second ferry is [tex]x_2=v_2t[/tex]
We want to know when they will be 6 miles apart. This means, if we call that distance d, that we want to know when the difference between their positions will be d, or [tex]x_1-x_2=d[/tex] (we know that at the beginning the position of the ferry 1 is of higher value than that of ferry 2 since it left before).
We use our previous formulas then:
[tex]d=x_1-x_2=v_1t-v_2t=(v_1-v_2)t[/tex]
Since we want the time, we do:
[tex]t=\frac{d}{v_1-v_2}[/tex]
And substitute our values:
[tex]t=\frac{6\ miles}{30\ miles/hour-24\ miles/hour}=\frac{6\ miles}{6\ miles/hour} =1\ hour[/tex]
