A cyclist travels the length of a bike path that is 225 miles long, ro

Hi and welcome to GMAT Club. Below is a solution for the question.

It can be done in another way but since you chose algebraic approach I'll proceed with it

Length of a path is 225 miles long, rounded to the nearest mile --> \(224.5\leq{distance}<225.5\);
The trip took him 5 hrs, rounded to the nearest hour --> \(4.5\leq{time}<5.5\);

Highest average rate is \(\frac{225.5}{4.5}\approx{50.1}\) (take the highest value of nominator and lowest value of denominator);
Lowest average rate is \(\frac{224.5}{5.5}\approx{40.8}\) (take the lowest value of nominator and highest value of denominator);

\(40.8<rate<50.1\).

Now, the question is: "the average speed must be between..." hence the range from correct answer choice MUST cover all possible values of rate, so must cover all the range: \(40.8<rate<50.1\). Only C does that: \((40)<40.8<rate<50.1<(51)\). D can not be the answer as if \(rate=40.9\) or if \(rate=50.01\) then these possible values of the average rate are not covered by the range from this answer choice, which is (41-50).

Answer: C.

Hope it's clear.