SOLUTION: A train leaves a station at 11am, heading north. Another train, 320 km away, leaves at the same time, heading south. The average speed of the train heading north is 20 km/hr faster

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Question 1111066: A train leaves a station at 11am, heading north. Another train, 320 km away, leaves at the same time, heading south. The average speed of the train heading north is 20 km/hr faster than that of the train heading south. If the trains pass each other at 1.30 pm, what was the average speed of the southbound train?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
11 AM to 1:30 PM is +2.5+ hrs
Let +s+ km/hr = the speed of the southbound train
+s+%2B+20+ km/hr is the speed of the nothbound train
Let +d+ km = distance traveled by southbound train
+320+-+d+ km = distance traveled by northbound train
---------------------------------------------------
Equation for the southbound train:
(1) +d+=+s%2A2.5+
Equation for nothbound train:
(2) +320+-+d+=+%28+s+%2B+20+%29%2A2.5+
--------------------------------
Plug (1) into (2)
(2) +320+-+2.5s+=+%28+s+%2B+20+%29%2A2.5+
(2) +320+-+2.5s+=+2.5s+%2B+50+
(2) +5s+=+320+-+50+
(2) +5s+=+270+
(2) +s+=+54+
The average speed of the southbound train
is 54 km/hr
-------------------
check:
(1) +d+=+54%2A2.5+
(1) +d+=+135+
and
(2) +320+-+2.5%2A54+=+%28+54+%2B+20+%29%2A2.5+
(2) +320+-+135+=+74%2A2.5+
(2) +185+=+185+
and
+135+%2B+185+=+320+ km
OK