Question

Two boats started to move towards each other from two boat stations, located 30 miles apart. One boat moved at a speed of 3 miles per hour, the other moved twice as fast. How soon will the boats meet?

Answer 1

The boats will meet in 3.33 hours.

Explanation:

The position of each boat can be modeled by a first order equation.

I am going to say that the first boat is at the position 0, and moving in the positive direction with a speed of 3 miles per hour. So

`A(t) = 0 + 3t`

They are moving in oppositie directions, and initially are 30 miles apart. This means that the second boat starts at the position 30, and moves in the negative direction at the rate of 6 miles an hour. So

`B(t) = 30 - 6t`

How soon will the boats meet?

This is t when:

`A(t) = B(t)`

`3t = 30 - 6t`

`9t = 30`

`t = (30)/(9)`

`t = 3.33`

The boats will meet in 3.33 hours.