SOLUTION: Two ships leave port at the same time. One sails south at 15 mi/h and the other sails east at 20 mi/h. Find the function that models the distance (D) between the ships in terms of
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Question 74813This question is from textbook College Algebra
: Two ships leave port at the same time. One sails south at 15 mi/h and the other sails east at 20 mi/h. Find the function that models the distance (D) between the ships in terms of the time [(t) in hours] elapsed since their departure.
This question is from textbook College Algebra
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
This is a Pythagorean theorem problem. The two ships are at the vertex of a right angle.
.
One ship sails east and the distance it is from the starting point is 20*t where t is the time
that it has been underway.
.
The other ship sails south which is at an angle of 90 degrees to the path of the ship that
is going east. The distance that it is from the starting point is 15*t where t is also the
time that it has been underway.
.
Both of these paths are the legs of a right triangle. The distance between the ships is
the hypotenuse of the triangle.
.
The Pythagorean theorem says that the sum of the squares of the two legs of a right triangle
is equal to the square of the hypotenuse of the triangle. In equation form this would be:
.
.
Where s represents the distance to the south of the starting point and e represents
the distance to the east of the starting point. D is the distance between the two ships.
.
Substituting the two distances the ships have sailed at time t we get:
.
.
Squaring the terms on the left side results in:
.
.
You can then add the two terms on the left side:
.
.
Then to solve for D, take the square root of both sides:
.
.
which reduces to:
.
and
.
In this case we can ignore the negative solution because a negative distance between
them really has no meaning.
.
So the distance between the two ships is 25 times the time in hours that the ships have
been sailing. If they have been moving for 1 hour the distance between them is 25 miles.
If they have been going for 2 hours, the distance between them is 25*2 = 50 miles.
And so on ...
.
Hope this helps you to understand the problem.
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