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 Milestone Muse (Posted on 2013-10-10)
Two cars leave simultaneously from points X and Y on the same road but in opposite directions. Their speeds are constant, and in the ratio 5 to 4 with the car leaving at X being the faster of the two.

The cars travel to and fro between X and Y. They meet for the second time at the 145th milestone and for the third time at the 201st milestone.

What are the respective milestones at X and Y?

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution | Comment 1 of 3

DEFDBL A-Z
FOR x = 0 TO 600
FOR y = 0 TO 600
IF x < y THEN low = x: high = y:  ELSE low = y: high = x
IF ABS(x - y) > 55 AND low < 145 AND high > 201 THEN
c5 = x: c4 = y
c5dir = 5 * SGN(y - x)
c4dir = 4 * SGN(x - y)
mtg = 0
good = 1
DO WHILE mtg < 3
c5 = c5 + c5dir
IF c5 < low THEN c5 = low + ABS(c5 - low): c5dir = -c5dir
IF c5 > high THEN c5 = high - (c5 - high): c5dir = -c5dir
c4 = c4 + c4dir
IF c4 < low THEN c4 = low + ABS(c4 - low): c4dir = -c4dir
IF c4 > high THEN c4 = high - (c4 - high): c4dir = -c4dir
IF c4 = c5 THEN
mtg = mtg + 1
IF mtg = 2 AND c4 <> 145 OR mtg = 3 AND c4 <> 201 THEN
good = 0
EXIT DO
END IF
END IF
LOOP
IF good THEN PRINT x, y
END IF
NEXT
NEXT

finds the milestones at 103 and 229

 Posted by Charlie on 2013-10-11 00:35:06

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