SOLUTION: Two people leave a town traveling in oposite directions. One person leaves at 11:00am driving at 48mph while the second person leaves at 3:00pm and drives at 55mph, At what time wi

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Question 696528: Two people leave a town traveling in oposite directions. One person leaves at 11:00am driving at 48mph while the second person leaves at 3:00pm and drives at 55mph, At what time will they be 604 miles part?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
How much of a head start does the 1st person have?
3:00 PM minus 11:00 AM is +4+ hrs
+48%2A4+=+192+ miles
Start a stop watch when the 2nd person leaves at 3 PM
Let +t+ = time on the stop watch
when they are +604+ mi apart
Let +d+ = The distance that the 2nd person has to
travel until they are +604+ mi apart
( they are already +192+ mi apart )
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1st person's equation:
(1) +604+-+192+-+d+=+48t+
2nd person's equation:
(2) +d+=55t+
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(1) +412+-+d+=+48t+
Substitute (2) into (1)
(1) +412+-+55t+=+48t+
(1) +103t+=+412+
(1) +t+=+4+
This is the time on the stop watch which started at 3 PM
They will be 604 miles apart at 7 PM
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check answer:
(1) +604+-+192+-+d+=+48%2A4+
(1) +604+-+192+-+d+=+192+
(1) +d+=+604+-+384+
(1) +d+=+220+
and
(2) +d+=55t+
(2) +d+=+55%2A4+
(2) +d+=+220+
OK
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The 2nd person travels 220 mi after 1st person
travels 192 mi and an additional +48%2A4+=+192+ mi
+220+%2B+192+%2B+192+=+604+
OK