• M0★

    A clock chimes on the hour a number of times equal to the hour, and also chimes once every 15 minutes, or quarter hour. If the face of the clock cannot be seen and the clock has chimed once, what is the longest time you might have to wait to be sure of knowing the time?

    I think it is 1 hr 45 mins, because if the time is 12:15 and the clock has chimed once, then you will have to wait 45 minutes until 1:00, but because the one singular chime doesn't mean that you will know the time, you have to wait one more hour until you know the time at 2:00, but the answer to the summer math worksheet that this question came from says the answer is 1 hr 30 mins.

  • M0★ M1★ M2 M3 M4 M5

    In the worst-case scenario, you hear the clock at 12:45. 7 chimes later, you'll know that is 1:45 because the next one will be at 2 o'clock.
    (edit: correct me if I'm wrong btw, this is my best shot)

  • MOD

    @patienttortoise Super close @ashila ! I think you meant that worse case scenario is hearing the clock at 12:15. But yes, the idea that you know it's 1:45 is exactly it. After it chimes for the 7th time at 1:45, you know for sure that it's 1:45 because there's no other interval where it can chime exactly once 7 times in a row. So you actually don't have to wait until 2:00 to know the time. Thus, 12:15 to 1:45 is 1 hr 30 mins.

  • M0★

    @quacker88 Alright! Thanks for the answer!