SOLUTION: A diesel train left Miami and traveled east. Three hours later a cattle train left traveling 10 km/h faster in an effort to catch up to it. After 15 hours the cattle train finally

Algebra ->  Test -> SOLUTION: A diesel train left Miami and traveled east. Three hours later a cattle train left traveling 10 km/h faster in an effort to catch up to it. After 15 hours the cattle train finally       Log On


   

Question 1071551: A diesel train left Miami and traveled east. Three hours later a cattle train left traveling 10 km/h faster in an effort to catch up to it. After 15 hours the cattle train finally caught up. Find the diesel train's average speed.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
How far does the diesel train get in 3 hrs?
Let +s+ = the speed of the diesel train in km/hr
+d%5B1%5D+=+s%2A3+ km
--------------------------
+15+ hrs after the diesel train's head start,
the cattle train catches up with it.
Let +d+ = distance in km the cattle train
travels until it catches the diesel train
Start a stop watch when the cattle train leaves
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Equation for diesel train:
(1) +d+-+d%5B1%5D+=+s%2A15+
Equation for cattle train:
(2) +d+=+%28+s+%2B+10+%29%2A15+
---------------------------
(1) +d+-+3s+=+15s+
(1) +d+=+18s+
Now plug (1) into (2)
(2) +18s+=+%28+s+%2B+10+%29%2A15+
(2) +18s+=+15s+%2B+150+
(2) +3s+=+150+
(2) +s+=+50+
and
+s+%2B+10+=+60+
The diesel train's speed is 50 km/hr
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check:
(1) +d+=+18s+
(1) +d+=+18%2A50+
(1) +d+=+900+ km
and
(2) +d+=+%28+s+%2B+10+%29%2A15+
(2) +d+=+60%2A15+
(2) +d+=+900+ km
OK
check math & get another opinion if needed