vipulgoyal wrote: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 hrs, rounded to the nearest hour, then his average speed must be between:
A) 38 and 50 mph
B) 40 and 50 mph
C) 40 and 51 mph
D) 41 and 50 mph
E) 41 and 51 mph

later

Any value LESS THAN HALFWAY between two integers is rounded DOWN.
Once we reach the halfway point between two integers, we round UP.

The length of a bike path that is 225 miles long, rounded to the nearest mile:
Thus, 224.5 ≤ d < 225.5.

The trip took him 5 hrs, rounded to the nearest hour:
Thus, 4.5 ≤ t < 5.5.

Slowest possible speed:
(least possible distance) / (greatest possible time) = (224.5)/(5.5) ≈ 40.8.
Since the greatest possible time cannot be quite be 5.5 hours, the average speed must be GREATER than 40.8 miles per hour.

Fastest possible speed:
(greatest possible distance) / (least possible time) = (225.5)/(4.5) ≈ 50.1.
Since the greatest possible distance cannot quite be 222.5 miles, the average speed must be LESS than 50.1 miles per hour.

Thus:
40.8 < rate < 50.1.

Since the rate can be 50.09 miles per hour, eliminate A, B and D, which say that the rate must be less than 50 mph.
Since the rate can be 40.9 miles per hour, eliminate E, which says that the rate must be greater than 41 mph.

The correct answer is C.

Hi Mitch,

I have two queries here

1. since the range are 224.5 ≤ d < 225.5. & 4.5 ≤ t < 5.5, rather then 225.5 and 5.5 we should take 225.4 and 5.4 in calculation, threw which range turns out to be 41.57<= x <=50.8 or 41<=x<=51 or E

2. now this range satisfy option c also, in that case we should take the precise range or superset range??