Estimating the Time
Time is a very important topic to study. We play games, our industries run, scientists perform experiments, we also perform different tasks with respect to time. In simple terms, time is ‘what a clock reads’. In ancient times, different methods were used to measure time. An hourglass or a sundial was the most commonly used method of knowing time.
Nowadays, we use an analog watch. The digital watch is also commonly used which shows time in an easy to read format.
What are some ways to tell Time?
To tell time from an analog watch is very interesting. Usually, in an analog clock, there are markings from 1 to 12 in a circular pattern. There are three hands of an analog clock. The smallest hand which runs the slowest is called the hour hand. The longest hand which runs the fastest is called the second hand. And the third hand between these two that revolves faster than the hour hand, and slower than the second hand, is called the minute hand. But nowadays, there are different types of analog watches and clocks, which may not have numbers or even the second hand!
We can start by knowing how a minute is completed in the case of an analog clock. The second hand makes one full rotation around the face of the clock starting from 12 and ending back at the same point. It is at this point that the minute hand moves ahead by one step. As the minute hand completes one complete rotation as the and reaches 12 after starting from 12, an hour is completed. Once an hour is completed, the hour hand moves from one number on the clock to the next.
So it takes 1 minute for the minute hand to move from one mark to the next.
And it takes 1 hour for the hour hand to move from one mark to the next.
The next step will be to look at a few examples of telling the time by looking at the hands on an analog clock.
If the hands of the clock are at this position initially, then
Step 1: Look at the hour hand first.
The hour hand is between the 4 and the 5.
So, the time that needs to be found is after 4 o’clock and before 5 o’clock.
Step 2: Look at the minute hand.
Count by 5s from 12 to 7 as we pass each mark on the clock (that is 1, 2, 3, 4,… and so on).
5 + 5 + 5 + 5 + 5 + 5 + 5 = 35
Now the minute hand is two places ahead of 7.
So we need to add two more minutes:
35 + 2 = 37
So, the time is 4:37.
Measurement of Elapsed Time?
Elapsed time is the time that has passed between an interval of time. Time is always moving forward. Time elapses while doing a task or even while we rest. If we go to school and return in the afternoon we can notice that several hours have elapsed. Finding the elapsed time on a clock is a very easy task.
Let us take an example of a clock as shown below,
and after some time the clock shows:
How do we find the elapsed time?
There are two ways to find the elapsed time:
First way:
Use an analog clock to count the minutes, an old analog clock with no batteries can be used, and a pencil to mark the start and end times. Here are some steps that would guide you:
Step 1: Draw the starting time.
Step 2: Mark the ending time.
Step 3: Count the minutes by 5s and 1s until you reach the ending time.
In this clock, the minute hand starts from 1 and stops at three places after 8. As we counted 5s, eight times till 8, then the elapsed time till 8 is, 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35 minutes.
Now the minute hand is three places beyond 8 so count 1 three times and add it to the previous time:
1 + 1 + 1 =3 and 35 + 3 = 38 minutes
So, the elapsed time is 38 minutes.
Another way of finding the elapsed time is by using a number line. Here are some steps that would help us understand this process:
Step 1: Plot the starting time on a number line.
Step 2: Count forward by 10s , 5s and 1s until you reach the ending time.
Step 3: Add the jumps to find the elapsed time.
So, from 2:05 to 2:15 we have 10 minutes,
from 2.15 to 2.25 we have 10 minutes
and finally from 2.35 to 2.45 we have 10 minutes.
Now moving forward from 2.35 to 2.40 we have 5 minutes
and from 2.40 to 2.43 we have 3 minutes.
If we add up all the minutes just found we will get :
10 + 10 + 10 + 5 + 3 = 38 minutes
So, the elapsed time once again, is 38 minutes.
Elapsed Time across an hour
We come across scenarios where we need to calculate elapsed time across an hour. This happens when the minute hand crosses the 12 mark. But the method of calculating elapsed time remains the same, as the numbers are just markings. We will follow the same rule of counting 10s, 5s and 1s. Let us look at some examples to understand this:
Solved Examples on Estimating Time
Example 1 : Find the elapsed time from 7:45 AM to 8:12 AM
First way:
Use an analog clock to count the minutes, an old analog clock with no batteries can be used, and a pencil to mark the start and end times. Here are some steps that would guide you:
Step 1: Draw the starting time.
Step 2: Mark the ending time.
Step 3: Count the minutes by 5s and 1s until you reach the ending time.
In this clock, the minute hand starts from 9 and stops at two places after 2. As we counted 5s, five times till 2, then the elapsed time till 2 is, 5 + 5 + 5 + 5 = 20 minutes.
Now the minute hand is two places beyond 2 so count 1 twice, and add it to the previous time:
1 + 1 = 2 and 25 + 2 = 27
So, the elapsed time from 7:45 AM to 8:12 AM is 27 minutes.
Another way of finding the elapsed time is by using a number line. Here are some steps which would help us understand this:
Step 1: Plot the starting time on a number line.
Step 2: Count forward until you reach the end time.
Step 3: Add the jumps to find the elapsed time.
So, from 7:45 to 8:00 we have 15 minutes,
from 8.00 to 8.12 we have 12 minutes
If we add up all the jumps then we get :
15 + 12 = 27 minutes
So, the elapsed time from 7:45 AM to 8:12 AM is 27 minutes.
Example 2:
Smith has 30 minutes to play outside before dinner. He has already played for 18 minutes. How much time does Smith have left to play?
Solution:
Smith is allowed only 30 minutes to play outside before dinner. He has already played for 18 minutes.
Time for which Smith already played (18 minutes) should be subtracted from 30 to find the time remaining for him to play
.
So, the time left for playing = 30 – 18
= 12 minutes.
Smith can play for 12 minutes more.
Example 3:
What is the time shown in the clock?
Solution:
Step 1: Look at the hour hand first.
The hour hand is between the 5 and 6.
So, it is after 5 o’clock and before 6 o’clock.
Step 2: Look at the minute hand.
Count by 5s from 12 to 2. We counted 5s twice from 12 to 2 as:
5 + 5 = 10,
Now the minute hand is also four places ahead of 2. So we will count four 1s :
1 + 1 + 1 + 1 = 4
So, the total number of minutes are, 10 + 4 = 14
So, the time is 5 :14
Example 3:
What is the time shown in the clock?
Solution:
Step 1: Look at the hour hand first.
The hour hand is between the 12 and the 1.
So, it is after 12 o’clock and before 1 o’clock.
Step 2: Look at the minute hand.
So, the time is 12:43.
Count by 5s from 12 to 1. We counted 5s eight times from 12 to 8:
5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 40
Now the minute hand is also three places ahead of 8. So we will count three 1s:
1 + 1 + 1 = 3
So, the total number of minutes are 40 + 3 = 43
So, the time is 12 :43 .
Example 4:
Cam boarded up a train at 3:55 PM and reached another station at 4:41 PM. Find the time elapsed by Cam from 3:55 PM to 4:41 PM.
Solution:
First method:
Use an analog clock to count the minutes. As mentioned earlier, an old analog clock with no batteries can be used, and a pencil to mark the start and end times. Here are some steps that would guide you:
Step 1: Draw the starting time.
Step 2: Mark the ending time.
Step 3: Count the minutes by 5s and 1s until you reach the ending time.
In this clock, the minute hand starts from 11(55 minutes) and stops at one place after 8(40 minutes). As we counted 5s, nine times till 8, then the elapsed time till 8 is, 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 45 minutes.
Now the minute hand is one place after 8, which shows 1 minute. Now let’s add it to the previous time:
45 + 1 = 46
So, the elapsed time from 3:55 AM to 4:41 AM is 46 minutes.
Another way of finding the elapsed time is by using a number line. Here are some steps which would help us understand this:
Step 1: Plot the starting time on a number line.
Step 2: Count forward until you reach the end time.
Step 3: Add the jumps to find the elapsed time.
So, from 3:55 to 4:00 we have 5 minutes,
from 4:00 to 4:41 we have 41 minutes.
If we add up all the jumps then we get :
45 + 1 = 46 minutes
So, the elapsed time from 3:55 PM to 4:41 PM is 46 minutes.
The relation between an hour and a minute is that 60 minutes make an hour. And, 60 seconds make a minute.
(a) 1 hour = 60 minutes
(b) 1 minute = 60 seconds
A stopwatch is a special clock that shows time spent during an event. It is generally used in sports like swimming, racing and so on, to check the time taken to finish a lap. It is called a stop watch because we can start and stop the watch according to our needs. We can also reset a stopwatch.