SOLUTION: A train X leaves Meerut at 5a.m and reaches Delhi at 9a.m. Another train Y leaves Delhi at 7a.m and reaches Meerut at 10:30a.m . At what time do the two trains cross one another?

Question 825045: A train X leaves Meerut at 5a.m and reaches Delhi at 9a.m. Another train Y leaves Delhi at 7a.m and reaches Meerut at 10:30a.m . At what time do the two trains cross one another?
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
A train X leaves Meerut at 5a.m and reaches Delhi at 9a.m. Another train Y leaves Delhi at 7a.m and reaches Meerut at 10:30a.m . At what time do the two trains cross one another?

Suppose it is N km from Meerut to Delhi

Train X travels N km in 4 hours, so X's speed is N/4 km/hr
Train Y travels N km in  or  hours, so Y's speed 
is N� = N� = 2N/7 km/hr 

Let t = the time after 7a.m. that train Y travels
Then, t+2 = the time after 5a.m. that train X travels
 

        |   speed � time  =  distance
-------------------------------------    
train X |    N/4  |  t+2  | (N/4)(t+2)     
train Y |   2N/7  |   t   |   2Nt/7

Equation:

   Train X's distance + Train Y's distance = N km

                     (t+2) +  = N

Multiply by LCM = 28

                     7N(t+2) + 8Nt = 28N

Divide by N

                       7(t+2) + 8t = 28  
                      7t + 14 + 8t = 28
                          15t + 14 = 28
                               15t = 14
                                 t = 14/15 hr = (14/15)�60 = 56 min.

56 minutes after 7a.m. is 7:56a.m. 

Edwin
[It is only 88 km from Meerut to Delhi, so both trains are very slow! :) ]

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