Two boats leave a dock at the same time. One boat travels south at 16 mi / hr and the other travels east at 12 mi /hr. After half an hour, how fast is the distance between the boats increasing? Let x be the distance the eastbound boat has traveled, y be the distance the southbound boat has traveled, and z be the distance between the boats. Write an equation that relates x, y, and z. Differentiate both sides of the equation found in the previous step with respect to t. dz dx dy dt dt dt (Do not simplify.) After half an hour, the distance between the boats is increasing at mi / hr.

Two boats leave a dock at the same time. One boat travels south at 16 mi / hr and the other travels east at 12 mi /hr. After half an hour, how fast is the distance between the boats increasing? Let x be the distance the eastbound boat has traveled, y be the distance the southbound boat has traveled, and z be the distance between the boats. Write an equation that relates x, y, and z. Differentiate both sides of the equation found in the previous step with respect to t. dz dx dy dt dt dt (Do not simplify.) After half an hour, the distance between the boats is increasing at mi / hr.

Elementary Algebra

17th Edition

ISBN:9780998625713

Author:Lynn Marecek, MaryAnne Anthony-Smith

Publisher:Lynn Marecek, MaryAnne Anthony-Smith

Chapter8: Rational Expressions And Equations

Section8.9: Use Direct And Inverse Variation

Problem 8.175TI: The distance that Brad travels varies directly with the time spent traveling. Brad travelled 660...

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Question

Two boats leave a dock at the same time. One boat travels south at 16 mi / hr and the other travels east at 12 mi / hr. After half an hour, how fast is the distance
between the boats increasing?
Let x be the distance the eastbound boat has traveled, y be the distance the southbound boat has traveled, and z be the distance between the boats. Write an
equation that relates x, y, and z.
Differentiate both sides of the equation found in the previous step with respect to t.
dz
dx
dy
=
+
dt
dt
dt
(Do not simplify.)
After half an hour, the distance between the boats is increasing at
mi / hr.

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