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

1 hour

Step-by-step 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=(d)/(v_1-v_2)`

And substitute our values:

`t=(6\ miles)/(30\ miles/hour-24\ miles/hour)=(6\ miles)/(6\ miles/hour) =1\ hour`