College Algebra & Trigonometry, 2018a

4.9. OPTIMIZATION 249
The distance between the two ships is measured along the diagonal. Because this
creates a right triangle, we can use the Pythagorean Theorem to represent the
distance between the ships.
Buoy
10 miles
12 mph
Ship #1
10 miles
d
Ship #2
7 mph
In this case the legs of the right triangle begin as 10 miles, but they get shorter
as the ships travel closer to the buoy. For Ship #1, the distance decreases by 12
miles every hour - this means that the first ship will pass the buoy in less than one
hour. The distance between Ship #1 and the buoy can be represented as (10−12t),
where t is the number of hours spent traveling. Similarly, the distance between
Ship #2 and the buoy can be represented as (10 − 7t).
So, using the Pythagorean Theorem, we can represent the distance between the
ships at any given time as:
d 2 =(10− 7t) 2 +(10− 12t) 2
or
d = √ (10 − 7t) 2 +(10− 12t) 2