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 34 miles per hour. the second ferry, the bird, travels at 24 miles per hour. in how many hours will the two ferries be 40 miles apart?

Answer-  In 4 hours the two ferries will be 40 miles apart.

Solution-

It is a relative speed problem.

The speed of the first ferry = 34 mph

The speed of the second ferry = 24 mph

Relative speed of the two ferries = 34 - 24 = 10 mph

Relative distance between the two ferries = 40 miles

We know that,

⇒

Part A) The function written in vertex form is

Part B) The vertex of the function is the point

Step-by-step explanation:

Part A) Write the function in vertex form

we know that

The equation of a vertical parabola in vertex form is equal to

where

(h,k) is the vertex of the parabola

In this problem we have

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Factor the leading coefficient

Complete the square. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

-----> function in vertex form

Part B) Name the vertex for the function

we have

The vertex of the function is the point

The parabola open upward, so the vertex is a minimum

see the attached figure to better understand the problem