Stage Four

 
Problem No. 5
Time Counts

 

Guess how long it would take you to count to 1 000 000 and record your guess.

 

Calculate how long it will take you to count from 1 to 1 000 000.

 

Hint: Break up the question into small workable units. Draw up a table and look for patterns.

E.g. Time how long it takes you to count from 1 000 to 1 050; from 121 050 to 121 200 and from 999 950 to 1 000 000.

 

Do you think you have lived for 1 million minutes? Calculate how long you have been alive in minutes.

 

 

All Stage 4 Problems

 

Reference: Signpost Mathematics Year 7

A McSeveny/R Conway/S Wilkes, Longman p50

 

 

There was only one answer that came in for this one, from Tom who I think comes from Bees Creek Primary School in the Northern Territory. His answer was:

2 hours!!!

I wanted to see if Tom was in the right ball park with this result...

So I started counting.

I did tests on groups of different sized numbers because as numbers become bigger they take longer to say. I counted 50 numbers. I kept it simple because we just wanted an approximation.

For numbers in the 1000s and below I tested with 1000 to 1050 and it took me 77 seconds.

For numbers in the 10000s I tested with 52450 to 52500 and it took me longer because these numbers take longer to say. It took me 122 seconds.

For numbers in the 100000s I used 121150 to 121200 and it took me 145 seconds.

Range
Total Numbers in this Range
Total Numbers/50
Time for count to 50 (sec)
Total time (sec)

Up to 10000

10000

10000/50 = 200
77
15400

10000 to 100000

90000

90000/50 = 1800
122
219600

100000 to 1000000

900000

900000/50 = 18000
145
2610000

Total

2860400

2860400 sec = 2860400/60 min

= 47673 min (approx.)

= 47673/60 hours

= 794.5 hours (approx.)

Which is close enough to 5 weeks!

Sorry Tom, not quite in your ball park of 2 hours!

 

To work out approximately how many seconds you have been alive, you would multiply your age by 365 (days in a normal year) then by 24 (hours in a day) then by 60 (minutes in an hour) then by 60 again (seconds in a minute).

For 13 years old: 13 x 365 x 24 x 60 x 60 = 409 968 000 sec

That's a lot of seconds!

Of course to get a more accurate result you need to work on a more accurate age, and take into account leap years. Go on, get to it!