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by chaitanya.mehrotra » Wed Jul 20, 2011 12:33 am
A cyclist travels the length of a bike path that is 225 miles long, rounded to the nearest
mile. If the trip took him 5 hours, rounded to the nearest hour, then his average speed must be between:
(A) 38 and 50 miles per hour
(C) 40 and 51 miles per hour
(E) 41 and 51 miles per hour
(B) 40 and 50 miles per hour
(D) 41 and 50 miles per hour

As per the solution in the book , If the cyclist rode 225 miles, rounded to the nearest mile, and took 5 hours, rounded to the nearest hour, he traveled between 224.5 miles and 225.5 miles, and took between 4.5 and 5.5 hours.

Doubt: How come we have taken 225.5 miles ? If round this it will become 226 thus max it can be 225.4 .
Similarly how come we have taken 5.5 hours ?If round this it will become 6 thus max hours could be 5.4 .
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by Anurag@Gurome » Wed Jul 20, 2011 1:01 am
chaitanya.mehrotra wrote:Doubt: How come we have taken 225.5 miles ? If round this it will become 226 thus max it can be 225.4 .
Similarly how come we have taken 5.5 hours ?If round this it will become 6 thus max hours could be 5.4 .
That is because if traveled path is 225 miles, rounded to the nearest mile, then he has traveled a distance which is larger than or equal to 224.5 miles and smaller than 225.5 miles. Note that in the opening end it is 'larger than or equal to' but in the closing end it is 'smaller than'. That is because in the closing end we can't fix a value for the actual distance traveled. It can be 225.499 miles or 225.499999999 miles or 225.49999....(infinite number of 9's) miles.

Hence, the proper way to bound the actual distance traveled (d) is 224.5 ≤ d < 225.5
And, similarly the proper way to bound the actual time taken (t) is 4.5 ≤ t < 5.5

Hence, his average speed (v) must be between (smallest distance)/(largest time) and (largest distance)/(smallest time).

Hence, (224.5/5.5) < v < (225.5/4.5) ---> 40.8 < v < 50.1 ---> 40 < v < 51

The correct answer is C.
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