SOLUTION: Karnataka Express leaves Bangalore at 5 p.m. and reaches Dharmavaram at 9 p.m. Kurla Express leaves Dharmavaram at 7 p.m. and reaches Bangalore at 10.30 p.m. What time do the train

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Karnataka Express leaves Bangalore at 5 p.m. and reaches Dharmavaram at 9 p.m. Kurla Express leaves Dharmavaram at 7 p.m. and reaches Bangalore at 10.30 p.m. What time do the train      Log On

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Question 625091: Karnataka Express leaves Bangalore at 5 p.m. and reaches Dharmavaram at 9 p.m. Kurla Express leaves Dharmavaram at 7 p.m. and reaches Bangalore at 10.30 p.m. What time do the trains cross one another?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the distance between the cities
Let +r%5B1%5D+ = the rate of the Karnataka Express
Let +r%5B2%5D+ = the rate of the Kurla express
How much of a head start does the Karnataka Express have?
from 5 PM to 7 PM
+d%5Bh%5D+=+r%5B1%5D%2A2+ ( any units for d[h] )
--------------
+r%5B1%5D+=+d%2F4+
+r%5B2%5D+=+d%2F3.5+ ( any units for d - same as d[h] )
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Start a stopwatch when the Kurla Express leaves. They will both
travel for the same time, +t+
--------------
Think of one train as standing still, and the other approaching
at the sum of their speeds. The moving train must cover
+d+-+2r%5B1%5D++=+d+-+2%2A%28d%2F4%29+
The sum of their speeds is:
+d%2F4+%2B+d%2F3.5+
-------------------
+2%2A%28+d%2F4+%29+=+%28+d%2F4+%2B+d%2F3.5+%29%2At+
+d%2F2+=+d%2A%28+1%2F4+%2B+1%2F3.5+%29%2At+
Divide both sides by +d+
+1%2F2+=+%28+1%2F4+%2B+2%2F7+%29%2At+
Multiply both sides by +28+
+14+=+%28+7+%2B+8+%29%2At+
+t+=+14%2F15+ hrs
+14%2F15%2A60+=+56+ minutes
They will meet at 56 minutes past 7
----------
check:
+2%2A%28+d%2F4+%29+=+%28+d%2F4+%2B+d%2F3.5+%29%2A%2814%2F15%29+
+15%2F2+=+14%2F4+%2B+14%2F3.5+
+15%2F2+=+7%2F2+%2B+8%2F2+
+15%2F2+=+15%2F2+
OK