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Thousands and Millions

Age 11 to 14
Challenge Level

Here are a few of the solutions we received:

Do human beings live for as long as a million hours?

Amy from Frances Bardsley School for Girls concluded that most of us don't:

24 hrs = 1 day
365 days = 1 year
24 x 365 = 8760 hrs in a year
8760 x 79 (that's the rough age humans live for) = 692,040 hours, so we do not live for 1million hours.

And students from Jumeirah Primary School came to the same conclusion:

No, because the average human lives for 80 years. This equals 700800 hours, which is less that 1000000.

Saad from JPS in Dubai worked out that just a few of us do:

24 hours = 1day.
24 hours x 365 = 8760 hours per year.
10 years = 87600 hours
50 years = 43800 hours
100 years = 876000 hours
105 years = 919800 hours
110 years = 963600 hours
112 years = 981120 hours
114 years = 998640 hours
114.10 years = 999516 hours
114.13years = 999788.8 hours
114.1551 years = 999998.676 hours
114.1552 years = 999999.52 hours
114.1553 years = 1000000.428 hours

If you have been alive for a million seconds, how many birthdays have you had?

Linden from HighdownSchool worked out that there would be no birthdays:

1000000 seconds / 60 =16667 mintues
16667 mintues / 60 = 278 hours
278 hours / 24 = 12 days
Birthdays = 0

Alex from Welsey Collegecame to the same conclusion:

You wouldn't have been able to have a birthday 1 million seconds ago because 1 year's worth of seconds are 31,622,400

How long would it take to count to a million?

Alex from Toot Hill's Junior Maths Academy (Mathletes) had a go at this problem:

I broke the numbers down into groups, because I needed to find the average for the time taken to say the different numbers of digits.

Time taken to read single digit numbers: 4 seconds for all 9 numbers

Time taken to read double digit numbers: 5 seconds for 10 numbers, so 45 seconds for all 90 numbers

Time taken to read triple digit numbers: 9 seconds for 10 numbers, so 810 seconds for all 900 numbers

Time taken to read four digit numbers: 18 seconds for 10 numbers, so 16200 seconds for all 9000 numbers

Time taken to read five digit numbers: 18 seconds for 10 numbers, so 162000 seconds for all 90000 numbers

Time taken to read six digit numbers: 23 seconds for 10 numbers, so 2070000 seconds for all 900000 numbers

Time taken to read seven digit number: 1 second for one number

So 2249060 seconds to countall one million numbers.

2249060 seconds is 37484.3 minutes which is 624.7 hours which is 26 days.

This would work if you make the assumptions:
that you talk at a constant speed;
that you don't eat or drink or sleep...!

Thank you all for your clear explanations.