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| A Refuel Time Problem (Posted on 2006-12-08) |
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At the precise instant when Mr. Ifield drove off from his residence in his car at a constant speed of 44 miles per hour; the minute hand of his 12 hour analog wristwatch was precisely on a minute mark.
After 3 miles of travel, Mr. Ifield stopped by a gasoline station to refuel when he observed that the minute hand and the hour hand of his wrist watch were exactly coincident but the minute hand was not precisely situated on a minute mark.
At what time did Mr. Ifield leave his residence?
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Submitted by K Sengupta
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Rating: 4.3333 (3 votes)
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Solution:
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(Hide)
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We know that in general, that minute hand and hour hand are coincident with the minute hand not exactly on a minute mark at (60*T /11) minutes past T o’clock, for T = 1,2,….10.
Since, Mr. Ifield drove for (3*60/44) = (4+ 1/11) minutes; it follows that (60*T -1)/ 11 must be an integer, for T = 1 to 10.
Clearly, only T =9 satisfies this condition, since 539 is divisible by 11.
Consequently, Mr. Ifield left his residence at (540/11 – 45/11) = 45 Minutes past 9 O’clock.
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