SOLUTION: Two persons are to run a race, but one can run 12 meters persecond, whereas the other can run 6 meters per second. If the slower runner has a 99-meter head start. how long will it

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Question 709865: Two persons are to run a race, but one can run 12 meters persecond, whereas the other can run 6 meters per second. If the slower runner has a 99-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!
Start a stop watch when the faster runner leaves
Let +d+ = the distance the faster runner has
traveled when the slower runner is caught
Let +t+ = the time in secods when the slower runner is caught
---------------
Faster runner's equation:
(1) +d+=+12t+
Slower runners equation:
(2) +d+-+99+=+6t+
-----------------
(2) +d+=+6t+%2B+99+
Substitute (1) into (2)
(2) +12t+=+6t+%2B+99+
(2) +6t+=+99+
(2) +t+=+16.5+
The time is 16.5 sec when the slower runner is caught
check:
(1) +d+=+12%2A16.5+
(1) +d+=+198+ m
and
(2) +d+-+99+=+6%2A16.5+
(2) +d+=+99+%2B+99+
(2) +d+=+198+ m
OK