SOLUTION: Need help please , Two trains travel round toy railway track, one takes 40 secs per circuit, the other takes 55 secs. How long before they are back in the station together?

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Question 634130: Need help please ,
Two trains travel round toy railway track, one takes 40 secs per circuit, the other takes 55 secs.
How long before they are back in the station together?
Look forward to a reply
Best regards and many thanks
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Since the length of the track isn't given,
I'll say it is +40+ units.
So the faster train's speed is +40+%2F+40+=+1+ unit/sec
The slower train's speed is +40%2F55+ units/sec
------------
I think of the round track as straightened out
with a mark on the track every +40+ units.
Then the problem becomes:
"What is the smallest time +t+ when they both
end up on a mark?" The mark is really the same point
repeated.
The faster train:
(1) +j%2A40+=+1%2At+
The slower train:
(2) +k%2A40+=+%2840%2F55%29%2At+
( j and k are whole numbers )
--------------------
Solving for t,
(1) +t+=+40j+
(2) +t+=+55k+
so, +40j+=+55k+
+j%2Fk+=+55%2F40+
+j%2Fk+=+11%2F8+
------------
This tells me the faster train goes around 11 times,
and the slower train goes around 8 times in time
+t+ , meeting back at the start
------------
(1) +t+=+40j+
(1) +t+=+40%2A11+
(1) +t+=+440+ sec
and, checking
(2) +t+=+55k+
(2) +t+=+55%2A8+
(2) +t+=+440+ sec