SOLUTION: one train starts from delhi 6 a.m reach to lucknow 10 a.m & other train starts from lucknow 8a.m reach to 11.30 a.m which time they reach each other

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Question 824331: one train starts from delhi 6 a.m reach to lucknow 10 a.m & other train starts from lucknow 8a.m reach to 11.30 a.m which time they reach each other
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The distance between the places doesn't matter.
Units of distance aren't given, so I'll say they
are +1+ unit apart ( any unit )
------------
10 AM minus 6 AM is +4+ hrs
The 1st train's rate is +1%2F4+ units/hr
-------------
11:30 AM minus 8 AM is +3.5+ hrs
The 2nd train's rate is +1%2F3.5+=+2%2F7+ units/hr
-------------
8 AM minus 6 AM is +2+ hrs
What is the 1st train's head start?
+d%5B1%5D+=+%281%2F4%29%2A2+
+d%5B1%5D+=+1%2F2+ units
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Start a stopwatch when the 2nd train leaves
Let +t+ = time in hrs on the stopwatch
when they meet
Let +d+ = the distance the 2nd train traveled
until they meet
--------------
1st train's equation:
(1) +%28+1-d+%29+-+%281%2F2%29+=+%281%2F4%29%2At+
2nd train's equation:
(2) +d+=+%282%2F7%29%2At+
-----------------
(1) +-d+%2B1%2F2+=+%281%2F4%29%2At+
(1) +-4d+%2B+2+=+t+
(1) +t+=+2+-+4d+
----------------
(2) +t+=+%287%2F2%29%2Ad+
By substitution:
(1) +%287%2F2%29%2Ad+=+2+-+4d+
(1) +7d+=+4+-+8d+
(1) +15d+=+4+
(1) +d+=+4%2F15+
----------------
(2) +t+=+%287%2F2%29%2Ad+
(2) +t+=+%287%2F2%29%2A%284%2F15%29+
(2) +t+=+14%2F15+ hrs
-------------------
They will meet at 8 AM plus +14%2F15+ hrs
+%2814%2F15%29%2A60+=+56+
They will meet at 8:56
check:
(1) +%28+1-d+%29+-+%281%2F2%29+=+%281%2F4%29%2At+
(1) +%28+1-4%2F15+%29+-+%281%2F2%29+=+%281%2F4%29%2A%2814%2F15%29+
(1) +11%2F15+-+1%2F2+=+7%2F30+
(1) +22%2F30+-+15%2F30+=+7%2F30+
(1) +7%2F30+=+7%2F30+
OK