SOLUTION: A diesel train left Washington traveling north four hours before a cattle train. The cattle train traveled in the opposite direction going 55 mph slower than the diesel train for

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Question 860612: A diesel train left Washington traveling north four hours before a cattle train. The cattle train traveled in the opposite direction going 55 mph slower than the diesel train for three hours after which time the trains were 635 miles apart. Find the diesel train's speed.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the diesel train in mi/hr
How far does the diesel train get in 4 hrs?
+d%5B1%5D+=+s%2A4+
Let +d+ = the distance the cattle car travels until
the trains are +635+ mi apart
------------------------------
If you start a stopwatch when the cattle train
leaves, it will show 3 hrs when the trains
are +635+ mi apart
Diesel's equation:
(1) +635+-+d+-+4s+=+s%2A3+
Cattle train's equation:
(2) +d+=+%28+s+-+55+%29%2A3+
----------------------
Substitute (2) into (1)
(1) +635+-+%28+s+-+55+%29%2A3+-+4s+=+3s+
(1) +635+-3s+%2B+165+-+4s+=+3s+
(1) +10s+=+800+
(1) +s+=+80+ mi/hr
and
+80+-+55+=+25+ mi9/hr
The diesel train's speed was 80 mi/hr
---------------------------------
check:
(1) +635+-+d+-+4s+=+s%2A3+
(1) +635+-+d+-+4%2A80+=+80%2A3+
(1) +635+-+d+-+320+=+240+
(1) +d+=+635+-+320+-+240+
(1) +d+=+75+ mi
and
(2) +d+=+%28+s+-+55+%29%2A3+
(2) +d+=+%28+80+-+55+%29%2A3+
(2) +d+=+75+
OK