Numerical Applications
Solve problems on the concept of average speed
Age of a person, hours in a day, duration of a cricket match, etc.– everything represents time. There are two main objects that tell us time: clock and calendar. Our ancestors used to calculate time by observing the position of the Sun. But that would not be possible during cloudy days and rainy seasons. In ancient times, people used different types of time-telling instruments like shadow clock, rope clock, water clock, candle clock and sand clock to determine time. Units of time Seconds, minutes, hours, days, weeks, months and years are different units of time. We can convert one unit into another by using the relations between them. Let us learn in detail about the units of time and their relations. The smallest possible unit of time is second. 60 seconds make 1 minute and 60 minutes make 1 hour. i.e., 1 minute = 60 seconds and 1 hour = 60 minutes In other words, 1 second = 160 minutes and 1 minute = 160 hour Using the above two relations, let us find out the relation between hours and seconds. We know that 1 hour = 60 minutes = 60 60 seconds [ 1 minute = 60 seconds] = 3600 seconds 1 hour = 3600 seconds There are 24 hours in a day, so we can convert days in terms of minutes or seconds as shown below: 1 day = 24 hours = 24 60 minutes [ 1 hour = 60 minutes] = 1440 minutes = 1440 60 seconds [ 1 minute = 60 seconds] = 86400 seconds i.e., 1 day = 24 60 minutes = 24 60 60 seconds So, we have the following: 1 minute = 60 seconds 1 second = 160 minutes 1 hour = 60 minutes = 3600 seconds 1 minute = 160 hour 1 second = 13600 hour 1 day = 24 60 minutes = 24 60 60 seconds Now, using the given relations, let us try to convert 18 minutes into seconds. We know that 1 minute = 60 seconds In order to convert 18 minutes into seconds, we need to multiply 18 by 60. 18 minutes = 18 60 minutes = 1080 minutes Now, let us convert 780 minutes into hours. We know that 1 minute = 160 hour In order to convert 780 minutes into hours, let us multiply 780 by 160. 780 minutes = 780 160 hours = 78060 hours = 13 hours 24 hour clock We usually denote time from 12 mid-night to 12 noon as A.M. (Latin: Ante meridiem) and the time from 12 noon to 12 mid-night as P.M. (Latin: Post meridiem). Look at the following times: 14:40 hours and 20:00 hours Such representation of times is shown by a 24 hour clock. In a 24 hour clock, 12 A.M. is represented as 00:00 hours and 12 P.M. is represented as 12:00 hours. The given tables shows the different formats of time (in A.M.) represented by a 12 hour clock and a 24 hour clock: 12 hour format 24 hour format 12 A.M. 00:00 hours 1 A.M. 01:00 hours 2 A.M. 02:00 hours 3 A.M. 03:00 hours 4 A.M. 04:00 hours 5 A.M. 05:00 hours 6 A.M. 06:00 hours 7 A.M. 07:00 hours 8 A.M. 08:00 hours 9 A.M. 09:00 hours 10 A.M. 10:00 hours 11 A.M. 11:00 hours Now, the given table shows the different formats of time (in P.M.) represented by a 12 hour clock and a 24 hour clock: 12 hour format 24 hour format 12 P.M. 12:00 hours 1 P.M. 13:00 hours 2 P.M. 14:00 hours 3 P.M. 15:00 hours 4 P.M. 16:00 hours 5 P.M. 17:00 hours 6 P.M. 18:00 hours 7 P.M. 19:00 hours 8 P.M. 20:00 hours 9 P.M. 21:00 hours 10 P.M. 22:00 hours 11 P.M. 23:00 hours It can be observed that from 1 P.M. to 11 P.M., the 24 hour time corresponding to the 12 hour time can be obtained by adding 12 to the hours column. Conversely, 12 hour time corresponding to 24 hour time for these times can be obtained by subtracting 12 from the hours column. Railway time Observe the following table: S.no Train Number Name of the Train Place of Departure Destination Departure Time Arrival Time 1. 16235 Mysore Express Tuticorin Madurai Junction 16:35 19:45 2. 12695 Trivandrum Express Chennai Central Salem Junction 15:25 20:10 3. 16860 Maq Chennai Express Coimbatore Junction Tiruchirapalli 15:50 21:50 4. 17229 Sabari Express Coimbatore Junction Salem Junction 16:35 19:25 The given table shows the details of various trains such as arrival time, departure time of a train and destination. Such type of table is known as railways time table. It can be observed that the railway timings are not expressed in the A.M. or P.M. They are expressed using 24 hour format. Thus, 24 hour clock timings are generally called railway timings. The timings expressed using A.M. or P.M. are called ordinary timings. In the above table, all the timings are more than 12:00 hours. So, these timings can be converted into ordinary timings by subtracting 12 hours from them. Also, ordinary timings (between 1 P.M. to 11 P.M.) can be converted into railway timings by adding 12 hours to them. Let us go through some examples to understand the concept better. Example 1: How many minutes are there in 480 seconds? Solution: We know that 1 second = 160 minutes 480 seconds = 480 160 minutes = 48060 minutes = 8 minutes Example 2: How many hours are there in 1080 minutes? Solution : We know that 1 minute = 160 hour 1080 minutes = 1080 160 hours = 108060 hours = 18 hours Example 3: Rohan watched a 2 hours 50 minutes long movie. For how many minutes did he watch the movie? Also, find the time in seconds. Solution: We know that 1 hour = 60 minutes 2 hours = 2 60 minutes = 120 minutes Now, 2 hours 50 minutes = 2 hours and 50 minutes = 2 hours + 50 minutes = 120 minutes + 50 minutes = 170 minutes Let us convert 2 hours and 50 minutes into seconds. 2 hours and 50 minutes = 170 minutes = 170 60 seconds [ 1 minute = 60 seconds] = 10200 seconds Example 4: In an examination, Sarita took 2 hours 40 minutes 45 seconds to solve the paper whereas Latika took 2 hours 59 minutes 30 seconds to solve the same paper. Who took more time to solve the paper and by how much (calculate in terms of seconds)? Solution: First, let us convert 2 hours 40 minutes 45 seconds into seconds. We know that 1 hour = 60 minutes 2 hours = 2 60 minutes = 120 minutes = 120 60 seconds [ 1 minute = 60 seconds] = 7200 seconds 40 minute = 40 60 seconds = 2400 seconds i.e., 2 hours 40 minutes 45 seconds = 2 hours + 40 minutes + 45 seconds = 7200 secon…
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