Final answer:
The first time that Mary's and Sue's clocks will chime together is after 45 minutes.
Step-by-step explanation:
To find the first time that Mary's and Sue's clocks will chime together, we need to determine the least common multiple (LCM) of 9 and 15. The LCM is the smallest number that is divisible by both 9 and 15. In this case, the LCM is 45. Therefore, their clocks will chime together for the first time after 45 minutes.