Answer: 48
There are many approaches to estimating stuff like this, so there isn't one set answer. My approach is shown below.
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1 min = 60 sec
30 min = 1800 sec (multiply both sides by 30)
1/2 hr = 1800 sec (replace "30 min" with "1/2 hr")
The value 2014 is fairly close to 1800, so roughly every half hour we have a prize being won. This is an overestimate.
There are 24 hours in a day, so 24*2 = 48 half-hour periods in a day, meaning we have an estimated 48 prizes in a full day. This is an overestimate as well.
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Extra info:
If you're curious about finding the more accurate value, then you could follow these steps
1 prize = 2014 seconds
x prizes = 86400 seconds (number of seconds in a full day)
1/x = 2014/86400
1*86400 = x*2014
86400 = 2014x
2014x = 86400
x = 86400/2014
x = 42.8997020854021
Round down to get x = 43. We round down because there isn't enough time to get that 44th prize. The value 43 is fairly close to 48, and we can see our earlier estimate of 48 was an overestimate.
