Musical maths
Approximately how long is five hundred and twenty five thousand six hundred minutes?
Age
11 to 14
Challenge level
Problem
The musical Rent contains a song which starts 'Five hundred and twenty five thousand six hundred minutes'.
Is this closest to a week, a month, a year, a decade or a century?
This problem is taken from the UKMT Mathematical Challenges.
Student Solutions
Answer: a year
Estimation
Number of hours:
525 600 $\div$ 60 = 52 560 $\div$ 6
$\approx$ 50 000 $\div$ 5
50 000 $\div$ 5 = 10 000
Number of days:
10 000 $\div$ 24 $\approx$ 10 000 $\div$ 25
10 000 $\div$ 25 = 100 $\times$ 100 $\div$ 25
= 100 $\times$ 4 = 400
Approximately 400 days is by far closer to a year than to a month or a decade.
Exact working
Number of hours:
525 600 $\div$ 60 = 8760
Number of days:
8760 $\div$ 24 = 365