SOLUTION: an accountant catches a train that travels at 50 miles per hour,whereas his boss leaves 1 hour later in a car traveling at 60 miles per hour.they had decided to meet at the train s

Algebra ->  Equations -> SOLUTION: an accountant catches a train that travels at 50 miles per hour,whereas his boss leaves 1 hour later in a car traveling at 60 miles per hour.they had decided to meet at the train s      Log On


   

Question 426000: an accountant catches a train that travels at 50 miles per hour,whereas his boss leaves 1 hour later in a car traveling at 60 miles per hour.they had decided to meet at the train station in the next town and, strangely enough, they get there at exactly the same time! If the train and car traveled in a straight line on parallel paths, how far is it from one town to the other?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The key is to find out how much of a head start the
accountant has. He gets a 1 hour head start at 50 mi/hr
+d%5B1%5D+=+50%2A1+
+d%5B1%5D+=+50+ mi is his head start
Now start a stopwatch when his boss leaves, and call
t the time when they meet at the station.
Let d = the distance the boss has to travel
+d+-+50+ will be the distance the accountant has to travel
-------------
For the accountant:
(1) +d+-+50+=+50t+
For the boss:
(2) +d+=+60t+
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Substitute (1) into (2)
(2) 60t+-+50+=+50t+
+10t+=+50+
+t+=+5+ hrs
Plug this back into (2)
(2) +d+=+60%2A5+
+d+=+300+
This is the entire distance that the boss has to travel,
so the towns are 300 miles apart
check answer:
The accountant goes d+-+50+=+250+ miles in t%7D%7D+hrs%0D%0A%281%29+%7B%7B%7B+d+-+50+=+50t+
(1) +250+=+50t+
+t+=+250%2F50+
+t+=+5+ hrs
OK