Math Skill: Time Intervals
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Time Intervals

In this topic, we will do calculations with time.

The clock below will help you. Count the number of hours clockwise (in the direction of the arrow) from the start time to the end time.

Example 1: A.M.

Solve.
How many hours are there from 6:13am to 10:13am?    hours

Since the minutes are the same (:13), we only look at the difference between the hours.

Solution: Counting
Using the clock above, we start at 6:00am and count clockwise to 10:00am.

 6:00 am   →   7:00 am   →   8:00 am   →   9:00 am   →  10:00 am Count: 1 hour 2 hours 3 hours 4 hours

Counting from 6:00am to 10:00am is 4 hours.

Alternate Solution: Subtraction
10:00am - 6:00am = 10 - 6 = 4 hours

Example 2: A.M. and P.M.

Solve.
If it is now 8:00 am, what time will it be in six and three-quarters hours?
:

8:00 am is 8 hours after the beginning of the day.
Six and three-quarters hours (6:45) after 8:00 am is
8:00 + 6:45 = 14:45

2:45 pm is 14 hours and 45 minutes after the beginning of the day.
14:45 = 2:45 pm

Alternate Solution: Counting
1. Count the hours
Using the clock above, we start at 8:00am and count 6 hours clockwise to 2:00pm.

 8:00 am   →  9:00 am   →  10:00 am   →  11:00 am   →  12:00 pm   →   1:00 pm   →   2:00 pm Count: 1 hour 2 hours 3 hours 4 hours 5 hours 6 hours

2. Count the minutes
Three-quarters of an hour = 45 minutes
From 2:00pm to 2:45pm is 45 minutes.

Example 3: next day

Solve.
What time was it eight hours before 3:00 am?
:

Solution: Subtraction
3:00 am is 3 hours after the beginning of the day.
Eight hours (8:00) before 3:00 am crosses into the previous day, so add 24 hours.
24:00 + 3:00 - 8:00 = 19:00

7:00 pm is 19 hours after the beginning of the day.
19:00 = 7:00 pm

Alternate Solution: Counting
Using the clock above, we start at 3:00am and count 8 hours (backwards or) counter-clockwise to 7:00pm.

 3:00 am   →  2:00 am   →  1:00 am   →  12:00 am   →  11:00 pm   →  10:00 pm   →   9:00 pm   →   8:00 pm   →   7:00 pm Count: 1 hour 2 hours 3 hours 4 hours 5 hours 6 hours 7 hours 8 hours

### Complexity=1, Mode=easy

Solve.
 1.   What time was it five hours before 9:00 pm? : --- am pm 2.   How much time is there from 12:00 am to 6:00 am? hours

### Complexity=1, Mode=medium

Solve.
 1.   What time was it twelve hours before 11:00 pm? : --- am pm 2.   How much time is there from 6:00 am to 2:00 pm? hours

### Complexity=1, Mode=hard

Solve.
 1.   What time will it be eleven hours past 3:00 pm? : --- am pm 2.   How many hours are there from 7:00 pm to 12:00 am (next day)? hours

### Complexity=2, Mode=medium

Solve.
 1.   How many hours and minutes are there from 9:00 am to 9:00 pm? hours minutes 2.   What time was it one and a half hours before 1:00 pm? : --- am pm

### Complexity=3, Mode=medium

Solve.
 1.   What time will it be seven and a quarter hours after 5:00 am? : --- am pm 2.   How many hours and minutes are there from 10:15 am to 3:30 pm? hours minutes

### Complexity=4, Mode=medium

Solve.
 1.   What time will it be eleven hours and 22 minutes after 6:43 am? : --- am pm 2.   What time was it six hours and 39 minutes before 2:28 pm? : --- am pm

### Complexity=4, Mode=hard

Solve.
 1.   How much time is there from 9:10 pm to 2:51 am (next day)? hours minutes 2.   What time was it four hours and 19 minutes before 1:26 am? : --- am pm

### Complexity=1, Mode=easy

Solve.
1What time was it five hours before 9:00 pm?
:
Solution
9:00 pm - 5:00 = 4:00 pm

Alternate Explanation:
Since the time you are looking for is in the past, count backwards.
Count the hours.

 9:00 pm → 8:00 pm → 7:00 pm → 6:00 pm → 5:00 pm → 4:00 pm Count: 1 hr 2 hr 3 hr 4 hr 5 hr
2How much time is there from 12:00 am to 6:00 am?
hours
Solution
12:00 am is midnight, which is the beginning of the day.
6:00 am is 6 hours after the beginning of the day.
6 hours - 0 hours = 6 hours

Alternate Explanation:
Count the hours.

 12:00 am → 1:00 am → 2:00 am → 3:00 am → 4:00 am → 5:00 am → 6:00 am Count: 1 hr 2 hr 3 hr 4 hr 5 hr 6 hr

### Complexity=1, Mode=medium

Solve.
1What time was it twelve hours before 11:00 pm?
:
Solution
11:00 pm to 11:00 am is exactly 12 hours apart.

Alternate Explanation:
11:00 pm is 23 hours after the beginning of the day.
Twelve hours (12:00) before 11:00 pm is
23:00 - 12:00 = 11:00

Alternate Explanation:
Since the time you are looking for is in the past, count backwards.
Count the hours.

 11:00 pm → 10:00 pm → 9:00 pm → 8:00 pm → 7:00 pm → 6:00 pm → 5:00 pm → 4:00 pm → 3:00 pm → 2:00 pm → 1:00 pm → 12:00 pm → 11:00 am Count: 1 hr 2 hr 3 hr 4 hr 5 hr 6 hr 7 hr 8 hr 9 hr 10 hr 11 hr 12 hr
2How much time is there from 6:00 am to 2:00 pm?
hours
Solution
Since the times cross from am to pm, use noon (12:00pm) to help us count the time.
6:00 am is 6 hours before noon.
2:00 pm is 2 hours after noon.

 Time difference = Time from 6:00 am to noon + Time from noon to 2:00 pm = 6 hours + 2 hours = 8 hours

Alternate Explanation:
Count the hours.

 6:00 am → 7:00 am → 8:00 am → 9:00 am → 10:00 am → 11:00 am → 12:00 pm → 1:00 pm → 2:00 pm Count: 1 hr 2 hr 3 hr 4 hr 5 hr 6 hr 7 hr 8 hr

Alternate Explanation:
6:00 am is 6 hours after the beginning of the day.
2:00 pm is 14 hours after the beginning of the day.

14 hours - 6 hours = 8 hours

### Complexity=1, Mode=hard

Solve.
1What time will it be eleven hours past 3:00 pm?
:
Solution
3:00 pm to 3:00 am is exactly 12 hours apart.
2:00 am is 1 hour before 3:00 am.
12 hours - 1 hour = 11 hours

Alternate Explanation:
3:00 pm is 15 hours after the beginning of the day.
Eleven hours (11:00) after 3:00 pm is
15:00 + 11:00 = 26:00

Since 26:00 > 24:00, the time has passed into the next day so subtract 24:00.
26:00 - 24:00 = 2:00 am

Alternate Explanation:
Count the hours.

 3:00 pm → 4:00 pm → 5:00 pm → 6:00 pm → 7:00 pm → 8:00 pm → 9:00 pm → 10:00 pm → 11:00 pm → 12:00 am → 1:00 am → 2:00 am Count: 1 hr 2 hr 3 hr 4 hr 5 hr 6 hr 7 hr 8 hr 9 hr 10 hr 11 hr
2How many hours are there from 7:00 pm to 12:00 am (next day)?
hours
Solution
Count the hours.
 7:00 pm → 8:00 pm → 9:00 pm → 10:00 pm → 11:00 pm → 12:00 am Count: 1 hr 2 hr 3 hr 4 hr 5 hr

Alternate Explanation:
7:00 pm is 19 hours after the beginning of the day.
12:00 am is midnight, which is the beginning of the day.
Since 12:00 am is in the next day, add 24 hours. (There are 24 hours in a day.)

0 hours + 24 hours - 19 hours = 5 hours

### Complexity=2, Mode=medium

Solve.
1How many hours and minutes are there from 9:00 am to 9:00 pm?
hours minutes
Solution
9:00 am to 9:00 pm is exactly 12 hours apart.

Alternate Explanation:
Since the times cross from am to pm, use noon (12:00pm) to help us count the time.
9:00 am is 3 hours before noon.
9:00 pm is 9 hours after noon.

 Time difference = Time from 9:00 am to noon + Time from noon to 9:00 pm = 3 hours + 9 hours = 12 hours

Alternate Explanation:
Count the hours.

 9:00 am → 10:00 am → 11:00 am → 12:00 pm → 1:00 pm → 2:00 pm → 3:00 pm → 4:00 pm → 5:00 pm → 6:00 pm → 7:00 pm → 8:00 pm → 9:00 pm Count: 1 hr 2 hr 3 hr 4 hr 5 hr 6 hr 7 hr 8 hr 9 hr 10 hr 11 hr 12 hr

Alternate Explanation:
9:00 am is 9 hours after the beginning of the day.
9:00 pm is 21 hours after the beginning of the day.

21 hours - 9 hours = 12 hours

2What time was it one and a half hours before 1:00 pm?
:
Solution
1:00 pm is 13 hours after the beginning of the day.
One and a half hours (1:30) before 1:00 pm is
13:00 - 1:30 = 11:30

Alternate Explanation:
Since the time you are looking for is in the past, count backwards.
1. Count the hours.

 1:00 pm → 12:00 pm Count: 1 hr
2. Count the minutes.
30 minutes before 12:00 pm is 11:30 am.

### Complexity=3, Mode=medium

Solve.
1What time will it be seven and a quarter hours after 5:00 am?
:
Solution
5:00 am is 5 hours after the beginning of the day.
Seven and a quarter hours (7:15) after 5:00 am is
5:00 + 7:15 = 12:15

Alternate Explanation:
1. Count the hours.

 5:00 am → 6:00 am → 7:00 am → 8:00 am → 9:00 am → 10:00 am → 11:00 am → 12:00 pm Count: 1 hr 2 hr 3 hr 4 hr 5 hr 6 hr 7 hr
2. Count the minutes.
From 12:00 pm to 12:15 pm is 15 minutes.
2How many hours and minutes are there from 10:15 am to 3:30 pm?
hours minutes
Solution
Since the times cross from am to pm, use noon (12:00pm) to help us count the time.
10:15 am is 1 hour and 45 minutes before noon.
3:30 pm is 3 hours and 30 minutes after noon.

 Time difference = Time from 10:15 am to noon + Time from noon to 3:30 pm = 1 hour and 45 minutes + 3 hours and 30 minutes = 5 hours and 15 minutes

Alternate Explanation:
1. Count the hours.

 10:15 am → 11:15 am → 12:15 pm → 1:15 pm → 2:15 pm → 3:15 pm Count: 1 hr 2 hr 3 hr 4 hr 5 hr
2. Count the minutes.
From 3:15 pm to 3:30 pm is 15 minutes.

Alternate Explanation:
10:15 am is 10 hours and 15 minutes after the beginning of the day.
3:30 pm is 15 hours and 30 minutes after the beginning of the day.

15 hours and 30 minutes - 10 hours and 15 minutes = 5 hours and 15 minutes

### Complexity=4, Mode=medium

Solve.
1What time will it be eleven hours and 22 minutes after 6:43 am?
:
Solution
6:43 am to 6:43 pm is exactly 12 hours apart.
6:05 pm is 38 minutes before 6:43 pm.
12 hours - 38 minutes = 11 hours and 22 minutes

Alternate Explanation:
6:43 am is 6 hours and 43 minutes after the beginning of the day.
Eleven hours and 22 minutes (11:22) after 6:43 am is
6:43 + 11:22 = 18:05

6:05 pm is 18 hours and 5 minutes after the beginning of the day.
18:05 = 6:05 pm

Alternate Explanation:
1. Count the hours.

 6:43 am → 7:43 am → 8:43 am → 9:43 am → 10:43 am → 11:43 am → 12:43 pm → 1:43 pm → 2:43 pm → 3:43 pm → 4:43 pm → 5:43 pm Count: 1 hr 2 hr 3 hr 4 hr 5 hr 6 hr 7 hr 8 hr 9 hr 10 hr 11 hr
2. Count the minutes.
From 5:43 pm to 6:05 pm is 22 minutes.
2What time was it six hours and 39 minutes before 2:28 pm?
:
Solution
2:28 pm is 14 hours and 28 minutes after the beginning of the day.
Six hours and 39 minutes (6:39) before 2:28 pm is
14:28 - 6:39 = 7:49

Alternate Explanation:
Since the time you are looking for is in the past, count backwards.
1. Count the hours.

 2:28 pm → 1:28 pm → 12:28 pm → 11:28 am → 10:28 am → 9:28 am → 8:28 am Count: 1 hr 2 hr 3 hr 4 hr 5 hr 6 hr
2. Count the minutes.
39 minutes before 8:28 am is 7:49 am.

### Complexity=4, Mode=hard

Solve.
1How much time is there from 9:10 pm to 2:51 am (next day)?
hours minutes
Solution
Since the times cross from pm to am, use midnight (12:00am) to help us count the time.
9:10 pm is 2 hours and 50 minutes before midnight.
2:51 am is 2 hours and 51 minutes after midnight.

 Time difference = Time from 9:10 pm to midnight + Time from midnight to 2:51 am = 2 hours and 50 minutes + 2 hours and 51 minutes = 5 hours and 41 minutes

Alternate Explanation:
1. Count the hours.

 9:10 pm → 10:10 pm → 11:10 pm → 12:10 am → 1:10 am → 2:10 am Count: 1 hr 2 hr 3 hr 4 hr 5 hr
2. Count the minutes.
From 2:10 am to 2:51 am is 41 minutes.

Alternate Explanation:
9:10 pm is 21 hours and 10 minutes after the beginning of the day.
2:51 am is 2 hours and 51 minutes after the beginning of the day.
Since 2:51 am is in the next day, add 24 hours. (There are 24 hours in a day.)

2 hours and 51 minutes + 24 hours - 21 hours and 10 minutes = 5 hours and 41 minutes

2What time was it four hours and 19 minutes before 1:26 am?
:
Solution
1:26 am is 1 hour and 26 minutes after the beginning of the day.
Four hours and 19 minutes (4:19) before 1:26 am crosses into the previous day, so add 24 hours.
24:00 + 1:26 - 4:19 = 21:07

9:07 pm is 21 hours and 7 minutes after the beginning of the day.
21:07 = 9:07 pm

Alternate Explanation:
Since the time you are looking for is in the past, count backwards.
1. Count the hours.

 1:26 am → 12:26 am → 11:26 pm → 10:26 pm → 9:26 pm Count: 1 hr 2 hr 3 hr 4 hr
2. Count the minutes.
19 minutes before 9:26 pm is 9:07 pm.