Aship sails for a distance of 150 nautical miles against a current, taking a total of 10 hours. if returns to the starting point, going with the current, in 6 hours. for both trips it moves the same speed through the water. a system of two equations can be used to find the speed of the ship and the current. let x represent the ship's speed and y represent the speed of the current. what is the correct equation for the ship's return going with the current?

x + y = 25 is the answer.

Step-by-step explanation:

Let the speed of the ship is represented by x and speed of current by y.

When the ship sails against the current the speed of ship will be (x - y) nautical miles per hour.

Against the current ship sails 150 nautical miles in 10 hours.

So the speed of the ship was =

                                                = nautical miles per hour

And the equation will be (x - y) =

x - y = 15 -------(1)

The same ship when returns with the current then the speed of the ship = (x + y)

Along with the current ship sailed the same distance 150 nautical miles in 6 hours.

Speed of the ship will be = nautical miles per hour

Now the second equation will be (x + y) = 25 --------(2)

Equation 2 is the equation represents ship's return while going with the current.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: