Math Problem Statement
The red car drives north at 62 miles per hour for 2 hours. The blue car drives east at 66 miles per hour for 2 hours.
Answer parts A-D below.
How far to the north has the red car traveled after 2 hours?
124 Correct miles
How far to the east has the blue car traveled after 2 hours?
132 Correct miles
Hint #1: Use the Pythagorean Theorem for parts C and D.
Hint #2: Part D is the related rates part of the question. Differentiate every term of the Pythagorean Theorem with respect to time, then plug in the calculated values for , , and found in parts A-C. You will also need to plug in the red and blue cars' rates (speeds) that were provided in the problem.
Round answers for parts C and D to 2 decimal places.
How far apart are the cars after 2 hours?
181.11 Correct miles
How fast is the distance between the cars changing?
mi/hr
Solution
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Math Problem Analysis
Mathematical Concepts
Distance Calculation
Pythagorean Theorem
Related Rates
Formulas
Distance = Speed × Time
Pythagorean Theorem: c^2 = a^2 + b^2
Related Rates: z * dz/dt = x * dx/dt + y * dy/dt
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 9-12
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