SOLUTION: two persons are to run a race, but one can run 8 meters per second, whereas the other can run 2 meters per second. If the slower runner has a 81 meter head start, how long will it

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Question 945183: two persons are to run a race, but one can run 8 meters per second, whereas the other can run 2 meters per second. If the slower runner has a 81 meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the distance in meters the faster runner travels
until the slower runner is caught
Let +t+ = time in seconds for faster runner to
catch slower runner
-----------------------
faster runner's equation:
+d+=+8t+
slower runner's equation:
+d+-+81+=+2t+
-----------------
By substitution:
+8t+-+81+=+2t+
+6t+=+81+
+t+=+13.5+
In 13.5 seconds the faster runner catches
the slower runner