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Amo slept from 8:20 pm to 5:00 am. How long did Amo sleep?

Mathematics

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Answer

8 hours 40 minutes\text{8 hours 40 minutes}

Step-by-step solution

3 steps

  1. Calculate the time Amo slept from 8:20 pm8:20 \text{ pm} until midnight.

    Midnight is 12:00 am12:00 \text{ am}.
    To find the duration from 8:20 pm8:20 \text{ pm} to 12:00 am12:00 \text{ am}, we subtract 8 hours 20 minutes8 \text{ hours } 20 \text{ minutes} from 12 hours 0 minutes12 \text{ hours } 0 \text{ minutes}.
    We need to borrow 1 hour1 \text{ hour} from 12 hours12 \text{ hours}, which is 60 minutes60 \text{ minutes}.
    So, 12 hours 0 minutes12 \text{ hours } 0 \text{ minutes} becomes 11 hours 60 minutes11 \text{ hours } 60 \text{ minutes}.

    11 hours 60 minutes−8 hours 20 minutes3 hours 40 minutes\begin{align*} &\quad 11 \text{ hours } 60 \text{ minutes} \\ &- \quad 8 \text{ hours } 20 \text{ minutes} \\ \hline &\quad 3 \text{ hours } 40 \text{ minutes} \end{align*}

    Amo slept for 3 hours 40 minutes3 \text{ hours } 40 \text{ minutes} before midnight.

  2. Calculate the time Amo slept from midnight until she woke up.

    Amo woke up at 5:00 am5:00 \text{ am}.
    The duration from 12:00 am12:00 \text{ am} to 5:00 am5:00 \text{ am} is 5 hours5 \text{ hours}.

  3. Add the durations from Step 1 and Step 2 to find the total sleep time.

    Total sleep time = 3 hours 40 minutes+5 hours 0 minutes3 \text{ hours } 40 \text{ minutes} + 5 \text{ hours } 0 \text{ minutes}

    3 hours 40 minutes+5 hours 0 minutes8 hours 40 minutes\begin{align*} &\quad 3 \text{ hours } 40 \text{ minutes} \\ &+ \quad 5 \text{ hours } 0 \text{ minutes} \\ \hline &\quad 8 \text{ hours } 40 \text{ minutes} \end{align*}

    Amo slept for a total of 8 hours 40 minutes8 \text{ hours } 40 \text{ minutes}.

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