SOLUTION: Thaddeus and Ian start at the same location and drive in opposite​ directions, but leave at different times. When they are 375 miles​ apart, their combined travel time is 9 hou

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Question 1158409: Thaddeus and Ian start at the same location and drive in opposite​ directions, but leave at different times. When they are 375 miles​ apart, their combined travel time is 9 hours. If Thaddeus drives at a rate of 40 miles per hour and Ian drives at a rate of 45 miles per​ hour, how long had each been​ driving?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the distance the slower one travels
+375+-+d+ = the distance the faster one travels
Let +t+ = the time the slower one travels
+9+-+t+ = the time the faster one travels
-----------------------
(1) +d+=+40t+
(2) +375+-+d+=+45%2A%28+9+-+t+%29+
------------------------------------
(2) +375+-+d+=+405+-+45t+
(2) +d+=+45t+-+30+
Substitute (1) into (2)
(2) +40t+=+45t+-+30+
(2) +5t+=+30+
(2) +t+=+6+
and
+9+-+t+=+3+
---------------------
The slower one travels for 6 hrs
The faster one travels for 3 hrs
---------------------
check:
(1) +d+=+40t+
(1) +d+=+40%2A6+
(1) +d+=+240+
and
(2) +375+-+d+=+45%2A%28+9+-+t+%29+
(2) +375+-+d+=+45%2A%28+9+-+6+%29+
(2) +375+-+d+=+45%2A3+
(2) +d+=+375+-+135+
(2) +d+=+240+
OK