SOLUTION: One bus route takes 25 minutes and the other bus route takes 55 minutes both buses leave the bus stop at 6 am and run continuously what is the next time that the buses will be at t

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Question 934859: One bus route takes 25 minutes and the other bus route takes 55 minutes both buses leave the bus stop at 6 am and run continuously what is the next time that the buses will be at the stop together ?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I want whole numbers +a+ and +b+
such that:
+25a+=+55b+
This is saying:
( route time for bus a ) x ( number of time a's route repeated ) =
( route time for bus b ) x ( number of time b's route repeated )
I know that this would be true:
+25%2A55+=+55%2A25+, so I can start with
+a+=+55+
+b+=+25+
Divide both a and b by +5+
+25%2A11+=+55%2A5+
This is ( total time for route a ) = ( total time for route b ), or
+275+=+275+
Add +275+ min to 6 AM
+275+%2F+60+=+4+%2B+35%2F60+
and
+6+%2B+4+%2B+35%2F60+ = 10:35 AM