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Two people are in a building with exit C. Person A is walking towards exit C in the direction south with a speed of 2 ft/sec. At the same time, person B who is east of exit C is running west towards exit C at 10 ft/sec in order to meet person A. At a certain moment, person A is 10 ft from exit C and person B is 50 ft from exit C.  Will person B meet person A at exit C or will person A go through exit C before person A gets there? Explain (does not require calculus).  Find the rate at the distance between person A and person B is changing when person A is 10 ft from exit C and person B is 50 ft from exit C.

Two people are in a building with exit C. Person A is walking towards exit C in the direction south with a speed of 2 ft/sec. At the same time, person B who is east of exit C is running west towards exit C at 10 ft/sec in order to meet person A. At a certain moment, person A is 10 ft from exit C and person B is 50 ft from exit C.  Will person B meet person A at exit C or will person A go through exit C before person A gets there? Explain (does not require calculus).  Find the rate at the distance between person A and person B is changing when person A is 10 ft from exit C and person B is 50 ft from exit C.

Elementary Geometry for College Students
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter8: Areas Of Polygons And Circles
Section8.5: More Area Relationships In The Circle
Problem 42E: A goat is tethered to a barn by a 12-ft chain. If the chain is connected to the barn at a point 6 ft...
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  1. Two people are in a building with exit C. Person A is walking towards exit C in the direction south with a speed of 2 ft/sec. At the same time, person B who is east of exit C is running west towards exit C at 10 ft/sec in order to meet person A. At a certain moment, person A is 10 ft from exit C and person B is 50 ft from exit C. 
    1. Will person B meet person A at exit C or will person A go through exit C before person A gets there? Explain (does not require calculus). 
    2. Find the rate at the distance between person A and person B is changing when person A is 10 ft from exit C and person B is 50 ft from exit C.
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