SOLUTION: Julie took 2 hours longer to drive 600 miles on the first day of a trip than she took to drive 500 miles on the second day. If her speed was the same both days, what was the driv

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Question 760016: Julie took 2 hours longer to drive 600 miles on the first day of a trip than she took to drive 500
miles on the second day. If her speed was the same both days, what was the driving time for
each day?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = her time in hrs for the 2nd day
+t+%2B+2+ = her time in hrs for the 1st day
+r+ = her speed on both days
----------------
1st day:
(1) +600+=+r%2A%28+t+%2B+2+%29+
2nd day:
(2) +500+=+r%2At+
----------------
This is 2 equations with 2 unknowns, so it's solvable
(2) +r+=+500%2Ft+
and, by substitution:
(1) +600+=+%28+500%2Ft+%29%2A%28+t+%2B+2+%29+
(1) +600+=+500+%2B+1000%2Ft+
(1) +100+=+1000%2Ft+
(1) +100t+=+1000+
(1) +t+=+10+
+t+%2B+2+=+12+
Her time for the 1st day was 12 hrs
Her time for the 2nd day was 10 hrs
check:
(1) +600+=+r%2A%28+t+%2B+2+%29+
(1) +600+=+r%2A%28+10+%2B+2+%29+
(1) +12r+=+600+
(1) +r+=+50+
and
(2) +500+=+r%2At+
(2) +500+=+r%2A10+
(2) +r+=+50+
OK