Carlos is training for the Olympics. His first training session lasted for one hour and he increases each training session by ten minutes every time. After fiteen sessions, how many minutes will be spend training?
one hour + 15*1/6 hour.
Now multiply by sixty to get minutes.
If you want the total number of minutes set it up as an arithmetic series,
the first term is 60
the common difference is 10 and the number of terms is 15
Use the sum of terms formula, then break the total minutes back down to hours and minutes.
To find the total number of minutes Carlos will spend training, we can calculate the sum of an arithmetic series.
The first term is 60 minutes (which is equivalent to 1 hour).
The common difference is 10 minutes, as Carlos increases each training session by an additional 10 minutes.
The number of terms is 15, representing the number of training sessions Carlos will have.
To find the sum of an arithmetic series, we can use the formula:
Sum = (n/2) * (2a + (n-1)d)
where:
n is the number of terms
a is the first term
d is the common difference
Plugging in the values for Carlos' training sessions:
Sum = (15/2) * (2 * 60 + (15-1) * 10)
Simplifying this equation:
Sum = (15/2) * (120 + 14 * 10)
= (15/2) * (120 + 140)
= (15/2) * 260
= 1950
So Carlos will spend a total of 1950 minutes training.
To break this down into hours and minutes, we can divide 1950 by 60:
1950 minutes / 60 minutes = 32 hours and 30 minutes
Therefore, Carlos will spend 32 hours and 30 minutes training.