Water lillies double in area every 24 hour. In spring there is one water lily on a lake. In sixty days, the lake is completely covered with lillies. how many days did it take to cover half the lake
Answer 58
Anish is right
To determine how many days it took to cover half the lake, let's work backwards from the information given.
We know that the water lilies double in area every 24 hours. This means that for each day, the coverage of the lake increases by a factor of 2.
In 60 days, the lake is completely covered with lilies. This means that each day, the area covered by lilies is doubled until it fills the entire lake.
Since it takes 60 days to cover the entire lake, we can conclude that on the 59th day, the lake was half covered. This is because when you double the coverage area one more time on the 60th day, it becomes fully covered.
Therefore, it took 59 days to cover half the lake with lilies.
1 2 4 8 16
1 2^1 2^2 2^3 2^(n-1)
a a2^1 a 2^2 ....
geometric sequence with
a = 1
r = 2
n = number of days
2^59 = area
2^x = 2^59/2
x = n-1 = 58 so 59 days
which we could have said right off
because if you cover the whole lake in 60 days then the day before you must have half the lake covered.