Question

Two ships leave port at the same time. One sails south at 21 mi/h, and the other sails east at 28 mi/h. Find a function that models the distance D between the ships in terms of the time t (in hours) elapsed since their departure.

Answer 1

Answer:  D(t) = 35t

Or you could write D = 35t, though the use of D(t) emphasizes we have a function.

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Explanation:

See the diagram below. This shows a right triangle with legs a = 21t and b = 28t to represent the distances each boat travels after t hours. The distance between them is the length of the hypotenuse c. Use the pythagorean theorem to solve.

$c = \sqrt{a^2+b^2}\\\\c = \sqrt{(21t)^2+(28t)^2}\\\\c = \sqrt{441t^2+784t^2}\\\\c = \sqrt{1225t^2}\\\\c = \sqrt{(35t)^2}\\\\c = 35t$

The function is D(t) = 35t

For each increase of an hour, the boats will separate by another 35 miles. Put another way, the distance between each boat is increasing by 35 mph.