SOLUTION: lightning mcqueen is racing mater in a race. mater is given a 2 hour head stanrt. lightning mcqueen travels 18 mph faster than mater.if lightning mcqueen catches up to mater after

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Question 916078: lightning mcqueen is racing mater in a race. mater is given a 2 hour head stanrt. lightning mcqueen travels 18 mph faster than mater.if lightning mcqueen catches up to mater after 5 hours, how far did each car travel?
Please answer in Rate x time = distance boxes thanks :)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = Mater's speed in mi/hr
+s+%2B+18+ = lightening McQueen's speed in mi/hr
-----------------
Start stopwatch when L.M. leaves
Let +d+ = distance in miles L.M travels
until he catches Mater
-----------------
Mater's head start is:
+d%5B1%5D+=+s%2A2+
------------------
Equation for Mater:
(1) +d+-+s%2A2+=+s%2A5+
Equation for L.M.
(2) +d+=+%28+s+%2B+18+%29%2A5+
----------------------
(2) +d+=+5s+%2B+90+
Substitute (2) into (1)
(1) +5s+%2B+90+-+2s+=+5s+
(1) +2s+=+90+
(1) +s+=+45+
and
+s+%2B+18+=+63+
------------------
L.M. traveled:
(1) +d+-+2s+=+5s+
(1) +d+=+7s+
(1) +d+=+7%2A45+
(1) +d+=+315+
----------------
Mater traveled:
+d%5B1%5D+%2B+225+
+90+%2B+225+=+315+
------------------
L.M. traveled 315 mi
Mater traveled 315 mi
--------------------
check:
(1) +d+-+s%2A2+=+s%2A5+
(1) +d+=+7s+
(1) +315+=+7%2A45+
(1) +315+=+315+
and
(2) +315+=+%28+s+%2B+18+%29%2A5+
(2) +315+=+%28+45+%2B+18+%29%2A5+
(2) +315+=+63%2A5+
(2) +315+=+315+
OK