SOLUTION: For part of the first year of a dog's life, its growth can be approximated using a linear function.Emilie has two puppies: a Border collie and a younger Saint Bernard.During a 4-we

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: For part of the first year of a dog's life, its growth can be approximated using a linear function.Emilie has two puppies: a Border collie and a younger Saint Bernard.During a 4-we      Log On


   

Question 1105031: For part of the first year of a dog's life, its growth can be approximated using a linear function.Emilie has two puppies: a Border collie and a younger Saint Bernard.During a 4-week period, the Border collie grows from 13.4 kg to 17 while the Saint Bernard grows from 6 kg to 12.4 kg.Suppose each dog grows at a constant rate.Will the dogs ever have the same mass?If so, approximately what is the mass?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The collie's weight is a straight line over the 4 wks
You are given 2 points on that line
The St. Bernard's weight is a straight line over the 4 wks
You are given 2 points on that line
---------------------------------------------------
Call the start of the 4 wk period +t+=+0+
Let +m+ = mass in kg
The 2 points for the collie:
( 0, 13.4 )
( 4, 17 )
The 2 points for the St. Bernard:
( 0, 6 )
( 4, 12.4 )
-------------------------------
Use the general point-slope formula:
For collie:
+%28+m+-+13.4+%29+%2F+%28+t+-+0+%29+=+%28+17+-+13.4+%29+%2F+%28+4+-+0+%29+
+%28+m+-+13.4+%29+%2F+t+=+3.6+%2F+4+
+%28+m+-+13.4+%29+%2F+t+=+.9+
+m+-+13.4+=+.9t+
+m+=+.9t+%2B+13.4+
-----------------------
For St. Bernard:
+%28+m+-+6+%29+%2F+%28+t+-+0+%29+=+%28+12.4+-+6+%29+%2F+%28+4+-+0+%29+
+%28+m+-+6+%29+%2F+t+=+6.4+%2F+4+
+%28+m+-+6+%29+%2F+t+=+1.6+
+m+-+6+=+1.6t+
+m+=+1.6t+%2B+6+
-----------------------
find the intersection of the lines:
Set the masses equal to eachother
+.9t+%2B+13.4+=+1.6t+%2B+6+
+.7t+=+7.4+
+t+=+10.57+
and
+m+=+1.6t+%2B+6+
+m+=+1.6%2A10.57+%2B+6+
+m+=+16.91+%2B+6+
+m+=+22.91+ kg
Their masses will both be 22.91 kg in 10.57 weeks
Check the math