Question

Two​ high-speed ferries leave at the same time from a city to go to the same island. The first​ ferry, the​ Cat, travels at 30 miles per hour. The second​ ferry, the​ Bird, travels at 24 miles per hour. In how many hours will the two ferries be 6 miles​ apart?

Answer 1

Answer:

1 hour

Explanation:

Since the definition of velocity is $v=x/t$, we can calculate the position at time t of an object moving at speed v with $x=vt$.

The position of the first ferry is $x_1=v_1t$

The position of the second ferry is $x_2=v_2t$

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 $x_1-x_2=d$ (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:

$d=x_1-x_2=v_1t-v_2t=(v_1-v_2)t$

Since we want the time, we do:

$t=\frac{d}{v_1-v_2}$

And substitute our values:

$t=\frac{6\ miles}{30\ miles/hour-24\ miles/hour}=\frac{6\ miles}{6\ miles/hour} =1\ hour$