Subjects algebra

Time Conversion

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1. **State the problem:** We need to add the given seconds and express the total in weeks, days, hours, minutes, and seconds (w:d:h:m:s). 2. **Add all the seconds:** $$80986 + 715493 + 85401 + 146354 + 148362 + 171704 + 96423 + 116094 + 38050 + 136072 + 69011 + 63854 = 1768800$$ seconds total. 3. **Convert seconds to weeks, days, hours, minutes, and seconds:** - 1 week = 7 days = 7 \times 24 \times 3600 = 604800 seconds - 1 day = 24 \times 3600 = 86400 seconds - 1 hour = 3600 seconds - 1 minute = 60 seconds 4. **Calculate weeks:** $$\text{weeks} = \left\lfloor \frac{1768800}{604800} \right\rfloor = 2$$ weeks 5. **Remaining seconds after weeks:** $$1768800 - 2 \times 604800 = 1768800 - 1209600 = 559200$$ seconds 6. **Calculate days:** $$\text{days} = \left\lfloor \frac{559200}{86400} \right\rfloor = 6$$ days 7. **Remaining seconds after days:** $$559200 - 6 \times 86400 = 559200 - 518400 = 40800$$ seconds 8. **Calculate hours:** $$\text{hours} = \left\lfloor \frac{40800}{3600} \right\rfloor = 11$$ hours 9. **Remaining seconds after hours:** $$40800 - 11 \times 3600 = 40800 - 39600 = 1200$$ seconds 10. **Calculate minutes:** $$\text{minutes} = \left\lfloor \frac{1200}{60} \right\rfloor = 20$$ minutes 11. **Remaining seconds after minutes:** $$1200 - 20 \times 60 = 1200 - 1200 = 0$$ seconds 12. **Final answer:** $$2\text{ weeks } : 6\text{ days } : 11\text{ hours } : 20\text{ minutes } : 0\text{ seconds}$$