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Phillip departed from town A with coordinates (1, 6) towards town B with coordinates (7, 6). At the same time Bruce headed from town B to town A. What are the coordinates of point C where they will meet if the ratio of Phillip's to Bruce's rates is 7:5, respectively?

Respuesta :

sqdancefan

Answer:

  (4.5, 6)

Step-by-step explanation:

The distance covered is proportional to the rate, so the distance from A to C compared to the distance from B to C will have the same proportion as Phillip's and Bruce's rates.

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setup

  (C -A)/(B -C) = 7/5 . . . . . distance is proportional to rates

solution

  5(C -A) = 7(B -C) . . . . multiply by 5(B -C)

  12C = 7B +5A . . . . . add 7C+5A

  C = (7B +5A)/12 = (7(7, 6) +5(1, 6))/12 = (49+5, 42+30)/12 = (4.5, 6)

Phillip and Bruce will meet at C(4.5, 6).

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