SOLUTION: At their top speeds, Lance Armstrong can cycle 130 miles in the same time it took Maurice Garin to cycle 80 miles. This is because Armstrong's top speed is 10mph faster than Garin'

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Question 494886: At their top speeds, Lance Armstrong can cycle 130 miles in the same time it took Maurice Garin to cycle 80 miles. This is because Armstrong's top speed is 10mph faster than Garin's. Find the top speed of each.
Answer by josmiceli(9817) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = Armstrong's top speed
Let b = Garin's top speed
You need 2 motion equations:
Armstrong's:
(1) +d%5Ba%5D+=+r%5Ba%5D%2At%5Ba%5D+
Garin's:
(2) +d%5Bg%5D+=+r%5Bg%5D%2At%5Bg%5D+
----------------
given:
+t%5Ba%5D+=+t%5Bg%5D+ hrs ( call them both t )
+d%5Ba%5D+=+130+ mi
+d%5Bg%5D+=+80+ mi
+r%5Ba%5D+=+r%5Bg%5D+%2B+10+ mi/hr
+r%5Bg%5D+=+r%5Ba%5D+-+10+ mi/hr
-------------
(1) +130+=+r%5Ba%5D+%2At+
(2) +80+=+%28+r%5Ba%5D+-+10+%29%2At+
From (1)
(1) +t+=+130%2Fr%5Ba%5D+
(2) +80+=+%28+r%5Ba%5D+-+10+%29%2A%28130%2Fr%5Ba%5D%29+
(2) +80+=+130+-+1300+%2F+r%5Ba%5D+
(2) +80r%5Ba%5D+=+130r%5Ba%5D+-+1300+
(2) +50r%5Ba%5D+=+1300+
(2) +r%5Ba%5D+=+26+ mi/hr
and,
+r%5Bg%5D+=+r%5Ba%5D+-+10+
+r%5Bg%5D+=+16+ mi/hr
Armstrong's top speed is 26 mi/hr
Garin's top speed is 16 mi/hr