Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![### Subtracting Time: Example Problem
#### Perform the following operation:
\[
\begin{array}{ccc}
\text{5 hours} & \text{21 minutes} & \text{22 seconds} \\
-\text{4 hours} & \text{57 minutes} & \text{51 seconds} \\
\end{array}
\]
### Step-by-Step Solution
1. **Write down the numbers to be subtracted:**
\[
\begin{array}{ccc}
\text{5 hours} & \text{21 minutes} & \text{22 seconds} \\
-\text{4 hours} & \text{57 minutes} & \text{51 seconds} \\
\end{array}
\]
2. **Align hours, minutes, and seconds in columns and begin the subtraction from the seconds column:**
\[
\begin{array}{ccc}
\text{5 hours} & \text{21 minutes} & \text{22 seconds} \\
-\text{4 hours} & \text{57 minutes} & \text{51 seconds} \\
\end{array}
\]
3. **Subtract the seconds:**
Since 22 seconds is less than 51 seconds, you need to borrow 1 minute (which equals 60 seconds) from the 21 minutes. This leaves you with 20 minutes and \( 22 + 60 = 82 \) seconds.
\[
\begin{array}{ccc}
\text{5 hours} & \text{20 minutes} & \text{82 seconds} \\
-\text{4 hours} & \text{57 minutes} & \text{51 seconds} \\
\end{array}
\]
Now subtract the seconds:
\[
82 \text{ seconds} - 51 \text{ seconds} = 31 \text{ seconds}
\]
4. **Subtract the minutes:**
Since 20 minutes is less than 57 minutes, you need to borrow 1 hour (which equals 60 minutes) from the 5 hours. This leaves you with 4 hours and \( 20 + 60 = 80 \) minutes.
\[
\begin{array}{ccc}
\text{4 hours} & \text{80 minutes} & & \\
-\text{4 hours} & \text{57 minutes} & & \\
\end](https://content.bartleby.com/qna-images/question/3a817796-b4be-478d-ba8b-56db553c444f/50461ff0-65e4-4537-936e-aa03f7bebd1e/iajcgwi_processed.png)
Transcribed Image Text:### Subtracting Time: Example Problem
#### Perform the following operation:
\[
\begin{array}{ccc}
\text{5 hours} & \text{21 minutes} & \text{22 seconds} \\
-\text{4 hours} & \text{57 minutes} & \text{51 seconds} \\
\end{array}
\]
### Step-by-Step Solution
1. **Write down the numbers to be subtracted:**
\[
\begin{array}{ccc}
\text{5 hours} & \text{21 minutes} & \text{22 seconds} \\
-\text{4 hours} & \text{57 minutes} & \text{51 seconds} \\
\end{array}
\]
2. **Align hours, minutes, and seconds in columns and begin the subtraction from the seconds column:**
\[
\begin{array}{ccc}
\text{5 hours} & \text{21 minutes} & \text{22 seconds} \\
-\text{4 hours} & \text{57 minutes} & \text{51 seconds} \\
\end{array}
\]
3. **Subtract the seconds:**
Since 22 seconds is less than 51 seconds, you need to borrow 1 minute (which equals 60 seconds) from the 21 minutes. This leaves you with 20 minutes and \( 22 + 60 = 82 \) seconds.
\[
\begin{array}{ccc}
\text{5 hours} & \text{20 minutes} & \text{82 seconds} \\
-\text{4 hours} & \text{57 minutes} & \text{51 seconds} \\
\end{array}
\]
Now subtract the seconds:
\[
82 \text{ seconds} - 51 \text{ seconds} = 31 \text{ seconds}
\]
4. **Subtract the minutes:**
Since 20 minutes is less than 57 minutes, you need to borrow 1 hour (which equals 60 minutes) from the 5 hours. This leaves you with 4 hours and \( 20 + 60 = 80 \) minutes.
\[
\begin{array}{ccc}
\text{4 hours} & \text{80 minutes} & & \\
-\text{4 hours} & \text{57 minutes} & & \\
\end
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