SOLUTION: A truck traveling at 40 kph and a car traveling at 50 kph leave town A at the same time and travel to a second town B. Upon reaching B, the car turned around immediately and travel

Algebra ->  Human-and-algebraic-language -> SOLUTION: A truck traveling at 40 kph and a car traveling at 50 kph leave town A at the same time and travel to a second town B. Upon reaching B, the car turned around immediately and travel      Log On


   

Question 1097767: A truck traveling at 40 kph and a car traveling at 50 kph leave town A at the same time and travel to a second town B. Upon reaching B, the car turned around immediately and traveled the same road toward A. Find the distance between the towns if the car will meet the truck 30 km from town B.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let d = the distance from A to B
+d+-+30+ = the distance in km the truck travels
until it meets the car
+d+%2B+30+ = the distance in km the car travels
until it meets the truck
Let +t+ = time in hrs until they meet
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The truck's equation:
(1) +d+-+30+=+40t+
The car's equation:
(2) +d+%2B+30+=+50t+
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subtract (1) from (2)
(2) +d+%2B+30+=+50t+
(1) +-d+%2B+30+=+-40t+
--------------------------
+60+=+10t+
+t+=+6+ hrs
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Plug this result back into either equation
(1) +d+-+30+=+40%2A6+
(1) +d+=+240+%2B+30+
(1) +d+=+270+
The distance between the towns is 270 km
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check:
(2) +d+%2B+30+=+50t+
(2) +270+%2B+30+=+50%2A6+
(2) +300+=+300+
OK