My friend and I start on opposite ends of a circular track. At the same time we start running in the same direction. I run at a constant pace of a lap every two minutes around the outside of the track (63 meters from the center) and my friend runs at a constant pace of a lap every three minutes around the inside of the track (61 meters from the center). When the angle formed by lines from my friend and myself to the center is at 7 and I am behind my friend, how fast is the distance between us decreasing? What if I were in front of my friend, how fast is the distance between us increasing?

My friend and I start on opposite ends of a circular track. At the same time we start running in the same direction. I run at a constant pace of a lap every two minutes around the outside of the track (63 meters from the center) and my friend runs at a constant pace of a lap every three minutes around the inside of the track (61 meters from the center). When the angle formed by lines from my friend and myself to the center is at 7 and I am behind my friend, how fast is the distance between us decreasing? What if I were in front of my friend, how fast is the distance between us increasing?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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My friend and I start on opposite ends of a circular track. At the same time we start running in
the same direction. I run at a constant pace of a lap every two minutes around the outside of
the track (63 meters from the center) and my friend runs at a constant pace of a lap every three
minutes around the inside of the track (61 meters from the center). When the angle formed by
lines from my friend and myself to the center is at 5 and I am behind my friend, how fast is the
distance between us decreasing? What if I were in front of my friend, how fast is the distance
between us increasing?

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Step 1: Given information

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Step 2: Expression for gap between two runners at time 't'.

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Step 3 :Rate of change of d(t)

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Step 4: Time when angle between R and S is 90 degree.

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Step 5: rate of change of gap at t = 1.5min, When R is leading S

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Step 6: rate of change of gap at t = 4.5min, when S is leading R

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