Question

Convert
(a) 16 hours 600 seconds into minutes
(b) 9 hours 360 seconds into minutes
(c) 2 days 180 minutes into hours
(d) 9 days 420 minutes into hours

Answer 1

Hint: We convert each of the given values of time into required time using the conversions of hours into minutes, minutes into seconds and days into hours. Use a unitary method to find the value of the number of given hours, days and seconds into required time value.
* 1 day has 24 hours in it
* 1 hour has 60 minutes
* 1 minute has 60 seconds

Complete step-by-step solution:
We convert each part one by one
(a) 16 hours 600 seconds into minutes:
We first convert 16 hours into minutes
Since 1 hour \[ = 60\] minutes
Use unitary method to convert 16 hours into minutes
\[ \Rightarrow 16\] hours\[ = 16 \times 60\] minutes
\[ \Rightarrow 16\] hours\[ = 960\] minutes………………..… (1)
Now we convert 600 seconds into minutes
Since \[60\] seconds \[ = 1\] minute
Multiply both sides by 10
\[ \Rightarrow 60 \times 10\] seconds \[ = 1 \times 10\] minutes
\[ \Rightarrow 600\] seconds \[ = 10\] minutes……………...… (2)
Now we add the minutes from both equations (1) and (2)
Total time in minutes \[ = 960 + 10\]
Total time in minutes \[ = 970\]
\[\therefore \]16 hours and 600 seconds is equal to 970 minutes
(b) 9 hours 360 seconds into minutes:
We first convert 9 hours into minutes
Since 1 hour \[ = 60\] minutes
Use unitary method to convert 9 hours into minutes
\[ \Rightarrow 9\] hours\[ = 9 \times 60\] minutes
\[ \Rightarrow 9\] hours\[ = 540\] minutes……………….… (3)
Now we convert 360 seconds into minutes
Since \[60\] seconds \[ = 1\] minute
Multiply both sides by 6
\[ \Rightarrow 60 \times 6\] seconds \[ = 1 \times 6\] minutes
\[ \Rightarrow 360\]seconds \[ = 6\]minutes……………..… (4)
Now we add the minutes from both equations (3) and (4)
Total time in minutes \[ = 540 + 6\]
Total time in minutes \[ = 546\]
\[\therefore \]9 hours and 360 seconds is equal to 546 minutes
(c) 2 days 180 minutes into hours:
We first convert 2 days into hours
Since 1 day \[ = 24\] hours
Use unitary method to convert 2 days into hours
\[ \Rightarrow 2\] days\[ = 2 \times 24\] hours
\[ \Rightarrow 2\] days\[ = 48\] hours……………...… (5)
Now we convert 180 minutes into hours
Since \[60\] minutes \[ = 1\] hour
Multiply both sides by 3
\[ \Rightarrow 60 \times 3\] minutes \[ = 1 \times 3\] hours
\[ \Rightarrow 180\] minutes \[ = 3\] hours……………….… (6)
Now we add the hours from both equations (5) and (6)
Total time in hours \[ = 48 + 3\]
Total time in hours \[ = 51\]
\[\therefore \]2 days and 180 minutes is equal to 51 hours
(d) 9 days 420 minutes into hours:
We first convert 9 days into hours
Since 1 day \[ = 24\] hours
Use unitary method to convert 9 days into hours
\[ \Rightarrow 9\] days\[ = 9 \times 24\] hours
\[ \Rightarrow 9\] days\[ = 216\] hours…………..… (7)
Now we convert 420 minutes into hours
Since \[60\]minutes \[ = 1\] hour
Multiply both sides by 7
\[ \Rightarrow 60 \times 7\]minutes \[ = 1 \times 7\] hours
\[ \Rightarrow 420\] minutes \[ = 7\] hours……………...… (8)
Now we add the hours from both equations (7) and (8)
Total time in hours \[ = 216 + 7\]
Total time in hours \[ = 223\]
\[\therefore \]9 days and 420 minutes is equal to 223 hours

Note: Many students get confused while converting the given values into required values as they have to calculate the value of single unit first and then multiply by complete quantity that is required, keep in mind we can clearly see from the numbers given to us that they are multiples of 60, so we directly multiply with the factors on both sides.