Find the time a clock reads using congruences and mod 12 arithmetic: show work! lal 53...

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Find the time a clock reads using congruences and mod 12 arithmetic: show work! lal 53 hours before it reads 5 oclock. (b) 4

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Answer 1

Answer #1

(a). Note that, 535 (mod 12) , and 5–5=0 12 (mod 12) . Hence, 53 hours before 5 o'clock, the clock reads 12 o'clock.

(b). As 79x12=948, 950 = 2 (mod 12) . So, 950 hours after 9 o'clock the clock will read 11 o'clock.

(c). As 58×12=696, 703 27 (mod 12) . Also 2-7= - 5 7 (mod 12) . Hence, 703 hours before 2 o'clock the clock will read 7 o'clock.

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