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Math - Radio Station Broadcast Range

by ross
(chicago)











































radio station KMAT in math city is 200 miles away from radio station KGEO in geometry city. Highway 7, is a straight road that connects the two cities. KMAT broadcasts can be received up to 150 miles in all directions from the station and KGEO broadcasts can be received up to 125 miles in all directions. How long(in Miles) is the part of the highway where both stations can be received?

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Feb 17, 2011
Math - Radio Station Broadcast Range
by: Staff


The question:

by Ross
(Chicago)

radio station KMAT in math city is 200 miles away from radio station KGEO in geometry city. Highway 7, is a straight road that connects the two cities. KMAT broadcasts can be received up to 150 miles in all directions from the station and KGEO broadcasts can be received up to 125 miles in all directions. How long(in Miles) is the part of the highway where both stations can be received?


The answer:

This is certainly a case where a picture is worth 1000 words.

Click the link below to see a diagram of the problem.

http://www.solving-math-problems.com/images/Radio-Station-Broadcast-Range-Overlap-01.png

x = distance where both stations can be received

x = distance from KMAT where overlap ends – distance from KMAT where overlap begins

distance from KMAT where overlap ends = broadcast range of station KMAT = 150 miles

distance from KMAT where overlap begins = 200 miles – broadcast range of station KGEO = 200 – 125 = 75 miles from KMAT

x = distance from KMAT where overlap ends – distance from KMAT where overlap begins

x = 150 miles – 75 miles

x = 75 miles


the final answer is: both stations can be received for a distance of 75 miles



Thanks for writing.


Staff
www.solving-math-problems.com


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