Rounding miles, and rounding hours

[bkw]

I have had problems rounding values in MGMAT SG3 p.187 problem 5.

"A cyclist travels the length of a bike path that is 225 miles long, rounded to the nearest mile. If the trip took him 5hours, rounded to the nearest hour..."

My rounding:
224.5 225 225.4
4.5 5 5.49(?)

MGMAT rounding:
224.5 225 225.5 <- shouldn't 225.5 be rounded to 226?
4.5 5 5.5

Could somebody please clarify what I made wrong when rounding in this problem?

[pemdas]

@bkw, in your example rounding to nearest means 224.5 225 225.5 can be +225 or +226

225.5 is right in the middle of both numbers +225 and +226

moreover, we can round numbers up, down, from zero, etc., rounding is just a mathematical operation

[goalevan]

The difference is in whether you use an open or a closed inequality:

224.5 miles <= distance < 225.5 miles
4.5 hours <= time < 5.5 hours

Just make sure not to alter closed vs. open throughout the problem, these are often very important.

I believe this MGMAT problem is asking for the range of possible integer rates, given distance and time.

min rate = min distance / max time
max rate = max distance / min time

224.5 / 5.5 = 40 9/11
225.5 / 4.5 = 50 1/9

40 9/11 <= rate < 50 1/9

Or with integers, 41 <= rate <= 50

[HeintzC2]

I have had problems rounding values in MGMAT SG3 p.187 problem 5.

"A cyclist travels the length of a bike path that is 225 miles long, rounded to the nearest mile. If the trip took him 5hours, rounded to the nearest hour..."

My rounding:
224.5 225 225.4
4.5 5 5.49(?)

MGMAT rounding:
224.5 225 225.5 <- shouldn't 225.5 be rounded to 226?
4.5 5 5.5

Could somebody please clarify what I made wrong when rounding in this problem?

It seems a lot of people have the same issue with these rounding problems. If you don't understand closed/open inequalities, just know that although 225.5 may round up to 226, 225.49999(9 repeating) rounds down to 225. So you can't stop your inequality at 225.4 as the allowable values actually come infinitesimally close to 225.5.