Time Systems and Elapsed Time

Time Conversions: 24-Hour Clock to 12-Hour Clock (+1 Hour)

Calculating the time one hour after a given time in 24-hour notation, expressed in 12-hour clock system ($\text{AM}/\text{PM}$):

• Given $15:00$: One hour after is $16:00$, which corresponds to $4:00\,\text{PM}$.
• Given $09:00$: One hour after is $10:00$, which corresponds to $10:00\,\text{AM}$.
• Given $22:00$: One hour after is $23:00$, which corresponds to $11:00\,\text{PM}$.
• Given $07:00$: One hour after is $08:00$, which corresponds to $8:00\,\text{AM}$.
• Given $18:00$: One hour after is $19:00$, which corresponds to $7:00\,\text{PM}$.
• Given $12:30$: One hour after is $13:30$, which corresponds to $1:30\,\text{PM}$.
• Given $00:45$: One hour after is $01:45$, which corresponds to $1:45\,\text{AM}$.
• Given $16:15$: One hour after is $17:15$, which corresponds to $5:15\,\text{PM}$.
• Given $10:00$: One hour after is $11:00$, which corresponds to $11:00\,\text{AM}$.
• Given $20:20$: One hour after is $21:20$, which corresponds to $9:20\,\text{PM}$.
• Given $14:40$: One hour after is $15:40$, which corresponds to $3:40\,\text{PM}$.
• Given $23:10$: One hour after is $00:10$, which corresponds to $12:10\,\text{AM}$.
• Given $06:00$: One hour after is $07:00$, which corresponds to $7:00\,\text{AM}$.
• Given $19:50$: One hour after is $20:50$, which corresponds to $8:50\,\text{PM}$.
• Given $11:35$: One hour after is $12:35$, which corresponds to $12:35\,\text{PM}$.
• Given $01:25$: One hour after is $02:25$, which corresponds to $2:25\,\text{AM}$.
• Given $17:45$: One hour after is $18:45$, which corresponds to $6:45\,\text{PM}$.
• Given $08:55$: One hour after is $09:55$, which corresponds to $9:55\,\text{AM}$.
• Given $21:30$: One hour after is $22:30$, which corresponds to $10:30\,\text{PM}$.
• Given $13:15$: One hour after is $14:15$, which corresponds to $2:15\,\text{PM}$.

Clock Face Readings and Equivalencies

Specific time readings in 12-hour and 24-hour systems:

• $17:00$ in 12-hour format is $5:00\,\text{PM}$.
• $12:12\,\text{PM}$ in 24-hour format is $12:12$.
• $2:10\,\text{AM}$ in 24-hour format is $02:10$.
• $20:30$ in 12-hour format is $8:30\,\text{PM}$.
• $8:21\,\text{AM}$ in 24-hour format is $08:21$.
• $13:30$ in 12-hour format is $1:30\,\text{PM}$.
• $6:53\,\text{AM}$ in 24-hour format is $06:53$.
• $4:30\,\text{AM}$ in 24-hour format is $04:30$.

Elapsed Time Word Problems and Step-by-Step Solutions

Problem 1: Reading Duration

• Problem: Emma began reading her favorite book at $09:25$ and finished at $12:40$. How long did she spend reading?
• Solution Breakdown:
  • $09:25 \rightarrow 10:25$ = $1\,\text{hour}$
  • $10:25 \rightarrow 11:25$ = $1\,\text{hour}$
  • $11:25 \rightarrow 12:25$ = $1\,\text{hour}$
  • Total full hours accumulated: $3\,\text{hours}$ ($09:25 \rightarrow 12:25$)
  • Remaining minutes: $12:25 \rightarrow 12:40$ = $40 - 25 = 15\,\text{minutes}$
• Total Time: $3\,\text{hours and } 15\,\text{minutes}$
• Sentence Answer: She spent $3\,\text{hours and } 15\,\text{minutes}$.

Problem 2: Train Ride Duration

• Problem: A train departed the station at $15:18$ and arrived at $19:55$. How long was the train ride?
• Solution Breakdown:
  • $15:18 \rightarrow 16:18$ = $1\,\text{hour}$
  • $16:18 \rightarrow 17:18$ = $1\,\text{hour}$
  • $17:18 \rightarrow 18:18$ = $1\,\text{hour}$
  • $18:18 \rightarrow 19:18$ = $1\,\text{hour}$
  • Total full hours accumulated: $4\,\text{hours}$ ($15:18 \rightarrow 19:18$)
  • Remaining minutes: $19:18 \rightarrow 19:55$ = $55 - 18 = 37\,\text{minutes}$
• Total Time: $4\,\text{hours and } 37\,\text{minutes}$
• Sentence Answer: It was $4\,\text{hours and } 37\,\text{minutes}$ long.

Problem 3: Science Fair Duration

• Problem: The school science fair opened at $08:30$ and closed at $15:15$. How many hours and minutes did the event last?
• Solution Breakdown:
  • $08:30 \rightarrow 14:30$ = $6\,\text{hours}$
  • $14:30 \rightarrow 15:00$ = $30\,\text{minutes}$
  • $15:00 \rightarrow 15:15$ = $15\,\text{minutes}$
  • Sum of minutes: $30\,\text{minutes} + 15\,\text{minutes} = 45\,\text{minutes}$
• Total Time: $6\,\text{hours and } 45\,\text{minutes}$
• Sentence Answer: It lasted $6\,\text{hours and } 45\,\text{minutes}$.

Problem 4: Cooking Class Duration

• Problem: A cooking class started at $10:45$ and ended at $13:20$. What was the duration of the class?
• Solution Breakdown:
  • $10:45 \rightarrow 12:45$ = $2\,\text{hours}$
  • $12:45 \rightarrow 13:00$ = $15\,\text{minutes}$ ($60 - 45 = 15$)
  • $13:00 \rightarrow 13:20$ = $20\,\text{minutes}$
  • Sum of minutes: $15\,\text{minutes} + 20\,\text{minutes} = 35\,\text{minutes}$
• Total Time: $2\,\text{hours and } 35\,\text{minutes}$
• Sentence Answer: It was $2\,\text{hours and } 35\,\text{minutes}$ duration long.

Problem 5: Bus Trip Duration

• Problem: A bus left the terminal at $06:17$ and arrived at the next city at $10:05$. How long was the bus trip?
• Solution Breakdown:
  • $06:17 \rightarrow 09:17$ = $3\,\text{hours}$
  • $09:17 \rightarrow 10:00$ = $43\,\text{minutes}$ ($60 - 17 = 43$)
  • $10:00 \rightarrow 10:05$ = $5\,\text{minutes}$
  • Sum of minutes: $43\,\text{minutes} + 5\,\text{minutes} = 48\,\text{minutes}$
• Total Time: $3\,\text{hours and } 48\,\text{minutes}$
• Sentence Answer: It was $3\,\text{hours and } 48\,\text{minutes}$ long.

Problem 6: Nap Duration

• Problem: Jason took a nap from $13:15$ to $19:00$. How long did he nap?
• Solution Breakdown:
  • $13:15 \rightarrow 18:15$ = $5\,\text{hours}$
  • $18:15 \rightarrow 19:00$ = $45\,\text{minutes}$ ($60 - 15 = 45$)
• Total Time: $5\,\text{hours and } 45\,\text{minutes}$
• Sentence Answer: He napped for $5\,\text{hours and } 45\,\text{minutes}$.

Problem 7: Flight Duration

• Problem: A flight took off at $23:30$ and landed at $02:15$ the next day. How many hours and minutes was the flight?
• Solution Breakdown:
  • $23:30 \rightarrow 00:00$ (midnight) = $30\,\text{minutes}$
  • $00:00 \rightarrow 02:00$ = $2\,\text{hours}$
  • $02:00 \rightarrow 02:15$ = $15\,\text{minutes}$
  • Sum of minutes: $30\,\text{minutes} + 15\,\text{minutes} = 45\,\text{minutes}$
• Total Time: $2\,\text{hours and } 45\,\text{minutes}$
• Sentence Answer: It was $2\,\text{hours and } 45\,\text{minutes}$ long.