SOLUTION: A bus passenger observes that a train moving in opposite direction passes him in 5 seconds; but moving in the same direction with him, it passes him in 45 seconds. Compare the spee

Algebra ->  Proportions -> SOLUTION: A bus passenger observes that a train moving in opposite direction passes him in 5 seconds; but moving in the same direction with him, it passes him in 45 seconds. Compare the spee      Log On


   

Question 906585: A bus passenger observes that a train moving in opposite direction passes him in 5 seconds; but moving in the same direction with him, it passes him in 45 seconds. Compare the speed of the bus with that of the train.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In opposite directions, add the speeds
The combined speeds are inversely proportional
to the time it takes to pass
(1) +s%5B1%5D+%2B+s%5B2%5D+=+k%2A%281%2F5%29+
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In the same direction, subtract the speeds:
Let s[2] be the speed of the train, which is faster
(2) +s%5B2%5D+-+s%5B1%5D+=+k%2A%281%2F45%29+
--------------------------
Add the equations:
+2s%5B2%5D+=+k%2A%28+1%2F5+%2B+1%2F45+%29+
+2s%5B2%5D+=+k%2A%28+9%2F45+%2B+1%2F45+%29+
+2s%5B2%5D+=+%28+10%2F45+%29%2Ak+
+s%5B2%5D+=+%285%2F45%29%2Ak+
--------------------
and
(1) +s%5B1%5D+%2B+s%5B2%5D+=+k%2A%281%2F5%29+
(1) +s%5B1%5D+%2B+k%2A%281%2F9%29+=+k%2A%281%2F5%29+
(1) +s%5B1%5D+=+k%289%2F45%29+-+k%2A%285%2F45%29+
(1) +s%5B1%5D+=+%284%2F45%29%2Ak+
-----------------------
( speed of bus ) / ( speed of train ) = +s%5B1%5D+%2F+s%5B2%5D+
+s%5B1%5D+%2F+s%5B2%5D+=+%28%28+4%2F45%29%2Ak%29+%2F+%28%285%2F45%29%2Ak%29+
+s%5B1%5D+%2F+s%5B2%5D+=+4%2F5+
+s%5B1%5D+=+%284%2F5%29%2As%5B2%5D+
The bus's speed is 4/5 of the trains speed
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Hope I got it
You might want a 2nd opinion, too