The answer to this question is 24/99. 0.24 with 24 repeating in fractional form is 24/99. You put a 9 in the denominator for every repeating digit.
To be able to compare the rates, we will write them in fraction form.
The fraction that represents Joe's rate is:

and the fraction that represents Bob's rate is:

Simplifying the above fractions, we get:

Since:

then Bob and Joe did not work at the same rate.
Answer:
No, Bob and Joe did not work at the same rate.