SOLUTION: Suppose that a cyclist began a 308 mi ride across a state at the western edge of the​ state, at the same time that a car traveling toward it leaves the eastern end of the

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Suppose that a cyclist began a 308 mi ride across a state at the western edge of the​ state, at the same time that a car traveling toward it leaves the eastern end of the       Log On


   



Question 1017401:
Suppose that a cyclist began a 308 mi ride across a state at the western edge of the​ state, at the same time that a car traveling toward it leaves the eastern end of the state. If the bicycle and car met after 5.5 hr and the car traveled 36.8 mph faster than the​ bicycle, find the average rate of each.
The car average rate is ___ mph?
The bicycle's rate is ____ mph?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the bicycle in mi/hr
+s+%2B+36.8+ = the speed of the car in mi/hr
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You can think of one of them moving at the sum
of their speeds and the other one standing still,
because they are moving towards eachother.
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The distance traveled will be the sum of the
distances each would have traveled
in +5.5+ hrs
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+308+=+%28+s+%2B+s+%2B+36.8+%29%2A5.5+
+308+=+2s%2A5.5+%2B+36.8%2A5.5+
+308+=+11s+%2B+202.4+
+11s+=+105.6+
+s+=+9.6+
and
+s+%2B+36.8+=+9.6+%2B+36.8+
+s+%2B+36.8+=+46.4+
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The speed of the bicycle is 9.6 mi/hr
The speed of the car is 46.4 mi/hr
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check answers:
For the bicycle:
+d%5B1%5D+=+9.6%2A5.5+
+d%5B1%5D+=+52.8+
For the car:
+d%5B2%5D+=+46.4%2A5.5+
+d%5B2%5D+=+255.2+
--------------------
+d+=+d%5B1%5D+%2B+d%5B2%5D+
+d+=+52.8+%2B+255.2+
+d+=+308+
OK