SOLUTION: Vince left Trout Creek driving at 40km/h. Sybil followed 2h later driving at 50km/h. How far down the road will Sybil overtake Vince?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Vince left Trout Creek driving at 40km/h. Sybil followed 2h later driving at 50km/h. How far down the road will Sybil overtake Vince?      Log On


   

Question 899706: Vince left Trout Creek driving at 40km/h. Sybil followed 2h later driving at 50km/h. How far down the road will Sybil overtake Vince?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Vince's head start is:
+d%5B1%5D+=+40%2A2+
+d%5B1%5D+=+80+ km
-------------------
start a stopwatch when Sybil leaves
Let +d+ = distance Sybil travels
until she overtakes Vince
------------------------------
Let +t+ = time it takes for her to
catch Vince
-----------------
Vince's equation:
+d+-+80+=+40t+
Sybil's equation:
+d+=+50t+
----------------
By substitution:
+50t+-+80+=+40t+
+10t+=+80+
+t+=+8+
--------------
and
+d+=+50t+
+d+=+50%2A8+
+d+=+400+
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Sybil overtakes Vince 400 km down the road
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check:
+d+-+80+=+40t+
+400+-+80+=+40%2A8+
+320+=+320+
OK