A bell tolls every 30 minutes on the hour and at half past the hour. How many times does the bell toll between the times of 11.45a.m. and 3.10p.m.?
To solve this problem, let's break it down into smaller intervals.
Between 11.45a.m. and 12.00p.m., the bell tolls once at half past the hour (11.30a.m.) but not at the hour (12.00p.m.).
Between 12.00p.m. and 1.00p.m., the bell tolls twice at the hour (12.00p.m. and 1.00p.m.) and once at half past the hour (12.30p.m.).
Between 1.00p.m. and 2.00p.m., the bell tolls twice at the hour (1.00p.m. and 2.00p.m.) and once at half past the hour (1.30p.m.).
Between 2.00p.m. and 3.00p.m., the bell tolls twice at the hour (2.00p.m. and 3.00p.m.) and once at half past the hour (2.30p.m.).
Between 3.00p.m. and 3.10p.m., the bell tolls once at the hour (3.00p.m.) but not at half past the hour (3.30p.m.).
Adding up the number of tolls in each interval:
1 + 2 + 1 + 2 + 1 + 2 + 1 = 10
Therefore, the bell tolls 10 times between the times of 11.45a.m. and 3.10p.m.