SOLUTION: 2 runners approaching each other on a straight line track have constant speed of 4.5 and 3.5 m/s when they are 100 m apart how long will it take for the runners to meet each other

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Question 682872: 2 runners approaching each other on a straight line track have constant speed of 4.5 and 3.5 m/s when they are 100 m apart how long will it take for the runners to meet each other and what position will they meet ??
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the distance in meters that the faster runner will
travel until they meet.
+100+-+d+ = the distance in meters the slower runner will
travel until they meet
Let +t+ = time from when they are +100+ m apart
until they meet
--------------------
Equation for faster runner:
(1) +d+=+4.5t+
Equation for slower runner:
(2) +100+-+d+=+3.5t+
--------------------
Substitute (1) into (2)
(2) +100+-+4.5t+=+3.5t+
(2) +8t+=+100+
(2) +t+=+12.5+
It will take the runners 12.5 hrs to meet
and
(1) +d+=+4.5t+
(1) +d+=+4.5%2A12.5+
(1) +d+=+56.25+
and
+100+-+d+=+100+-+56.25+
+100+-+d+=+43.75+
The faster runner runs 56.25 m
The slower runner runs 43.75 m
check:
(2) +100+-+d+=+3.5t+
(2) +100+-+56.25+=+3.5%2A12.5+
(2) +43.75+=+43.75+
OK