SOLUTION: Curtis will run 4 miles the first week of training and increase the mileage by one mile each week. With another schedule, Curtis will run 1 mile the first week and increase his tot

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Curtis will run 4 miles the first week of training and increase the mileage by one mile each week. With another schedule, Curtis will run 1 mile the first week and increase his tot      Log On


   

Question 1018638: Curtis will run 4 miles the first week of training and increase the mileage by one mile each week. With another schedule, Curtis will run 1 mile the first week and increase his total mileage by 2 miles each week. During what week do the two schedules break even? How many miles will Curtis run during this week?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +y+ = miles run on week +x+
Let +m+ = the increase in milage each week
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1st schedual:
+y+=+m%2Ax+%2B+b+
+y+=+1%2Ax+%2B+4+
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2nd schedual:
+y+=+2x+%2B+1+
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Set the miles run equal to eachother
+x+%2B+4+=+2x+%2B+1+
+x+=+3+
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On week 3, they run the same miles
with either schedual
+y+=+1%2Ax+%2B+4+
+y+=+3+%2B+4+
+y+=+7+
and
+y+=+2x+%2B+1+
+y+=+2%2A3+%2B+1+
+y+=+7+
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On week 3, the miles run are the same
and Curtis runs 7 miles