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Conceptual Problems of Time And Mass

 Key Concepts

  • Minutes Hand
  • Hours Hand
  • Elapsed Time
  • A.M.
  • P.M.
  • Time Interval

Introduction

You are going to attempt the test on Mathematics. You have been informed that the test is of 90 minutes duration, and it begins at 9:00 A.M.

  1. What does it mean?
  2. What can we conclude?
  3. What is Time?

To understand the topic of time, we must learn the terms like minutes hand, hour’s hand.

The day is divided into 24 hours. The 24 hours are divided into two parts. The first 12 hours are called A.M., and the second 12 hours are called P.M.

Each hour is divided into 60 parts, and each part is called a minute.

Each minute is divided into 60 parts, and each part is called a second.

The clock we use has 12 numbers on it.

14.1 Time to the minute

The division of hours, minutes and seconds is known to us. The clock will have two pointers. We call them hands. The shorter pointer(hand) is called an hour’s hand, and the longer pointer(hand) is called a minutes hand.

14.1.1 Hour’s Hand and Minutes Hand

Between any two numbers, we have 5 parts as 12 x 5 = 60. As for every hour, we have 60 minutes. The minute’s hand moves 1 part. In one complete rotation of the minute’s hand, the hour’s hand move just one number that is 5 parts.

Clock = 12 parts(numbers)

Between each number we have 5 parts (12 x 5 = 60).

One complete rotation of minutes (longer) hand = Moving of one number of hours (shorter) hand.

= Moving of shorter (hours) hand 5 parts.

14.1.2 Study of Time

The study of time is observed on the clock. The representation of time can be done in two ways. In 24 hours format or 12 hours format. The conversion of the time from one format to the other can be done.

The conversion is simple. The first 12 hours are the same for both representations. But after the 12th hour in 24 hours format, we write it as 13:00. In 12 hours format, we begin again from 1:00

The representation of the time is HH : MM : SS or HH : MM or HH : MM. Here, H means hours, M means minutes, and S means seconds.

14.2 Units of Time: Measure Elapsed Time

The word elapsed means the difference between two times is called the elapsed time. In finding the difference, we even call it duration. In finding the time it took to run the field, bake the cake. All such things require time, and if the start time is given, the calculation of the end time be done.

14.2.1 A.M., P.M., and Elapsed Time

A.M. As we all know, the division of the 24 hours clock into two halves. The time from midnight to mid-noon is considered as A.M. The abbreviation of the A.M. is ‘ante meridiem’.

P.M. The time after mid-noon to midnight is considered as P.M. The abbreviation of the P.M. is ‘post meridiem’.

14.2.2 Counting of Hours and Minutes

The difference of time, initially we treat the time as a number and subtract. We study it with an example.

Example: The show starts at 9:30 A.M. The duration of the show is 2 hours and 45 minutes. What will be the end time of the show?

Solution: Treat the time 9:30 as the number 9.30 and the time to be added as 2.45. The addition is the same as the addition of the decimals.

9.30
+ 2.45
———–
11.75
———–

Every 60 minutes is one hour. So we subtract 60 from the minute’s section and add 1 to the hour’s section. That makes the minutes section with 15 and the hours section with 12.

So, the time will be 12.15. The show ends at 12:15.

14.2.3 Time Interval

Time interval is the difference between two times. We do the calculation in the same manner as we did the addition of the time.

14.3 Units of Time: Solve Word Problems

14.3.1 Word Problems on Time Interval

Example: Sarah started her homework at 5:30 P.M. and finished it at 9:15 P.M. How much time did she take to finish her homework?

Solution: The homework started at 5:30, making it the nearest hour by adding 30 minutes to make it 6:00.

The homework is finished at 9:15, from 6:00 to 9:00. We have 3 hours to 9:15. We have extra 15 minutes.

In total, the time taken is 30 minutes + 3 hours + 15 minutes

3 hours and 45 minutes

Exercise:

  1. A chef wants to bake the cake for 40 minutes. The cake has been baking for 19 minutes. How much more time is needed to bake?
  2. A movie starts at 5:00 P.M. and is having a duration of 2 hours and 30 minutes, and a break of 15 minutes. At what time does the movie end?
  3. In a relay, the first athlete covered the distance in 1 min and 23 sec. The second athlete covered the distance in 56 sec, and the final athlete covered the distance in 1 min 15 sec. The total time taken by the three athletes is how much?
  4. The time interval between 2:45 to 6:15 is
  5. Each lecture in school is of 50 minutes duration. If the class has 5 such lectures all day. Then the total time spent on the lectures is

What we have learned:

  • What is Minutes hand?
  • What is Hours hand?
  • What is Elapsed time?
  • What is A.M?
  • What is P.M?
  • What is a time interval?
  • Calculating the time interval.
  • Word problems on time.

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