SOLUTION: North train leaves at 1:00pm, South train leaves 1:00 pm, trains are 556 miles apart, 30 minutes later the trains pass each other, the north train is traveling 1.586 times faster t

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Question 856563: North train leaves at 1:00pm, South train leaves 1:00 pm, trains are 556 miles apart, 30 minutes later the trains pass each other, the north train is traveling 1.586 times faster than the south train, what are the speeds of the trains?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the south train travels
+556+-+d+ = distance the north train travels
Let +s+ = the speed of the south train
----------------
N. train's equation:
(1) +556+-+d+=+1.586s%2A%281%2F2%29+
S. train's equation:
(2) +d+=+s%2A%281%2F2%29+
---------------------------
Substitute (2) into (1)
(1) +556+-+s%2A%281%2F2%29+=+1.586s%2A%281%2F2%29+
(1) +556+=+.793s+%2B+.5s+
(1) +1.293s+=+556+
(1) +s+=+430.008+
+1.586%2A430.008+=+681.99+
--------------------------
The speeds of the trains are:
430 mi/hr and 682 mi/hr
check:
(1) +556+-+d+=+1.586%2A430%2A%281%2F2%29+
(1) +556+-+d+=+341+
(1) +d+=+215+
and
(2) +d+=+s%2A%281%2F2%29+
(2) +d+=+215+
OK