As part of a fitness program, Annie walks for 35 mins on day 1, and increases the walking time by 8 mins each day. She completes the fitness program on the day she first spends more than 3 hours walking. The program is completed on what day?
This is how I did it.
3 hours would be equal to 180 mins.
180 = 35 + (n-1)(8)
180 = 35 + 8n-8
180 = 27 + 8n
153 = 8n = 19.125. If I round that, then it would be 20. So I had to round it to get an answer, am I supposed to get a whole number in the starting?
Yes. They ask what day. That would be day 20. At the end of day 19, she still had not walked for 3 hours.
They didn't ask at what point she had walked three hours, but rather the day number.
Actually, you made a mistake in your calculation. Let's correct it step by step:
To find out on which day Annie completes the program, we need to determine when she first spends more than 3 hours walking, which is equal to 180 minutes.
Let's represent the number of days as 'n', and each day she walks for 35 minutes, and increases the walking time by 8 minutes each day.
On day 1, Annie walks for 35 minutes, so the total walking time is 35 minutes.
On day 2, Annie walks for 35 minutes + 8 minutes = 43 minutes.
We can see that her total walking time is increasing by 8 minutes each day.
To find out on which day she completes the program, we can set up an equation:
35 + 8(n-1) > 180
Now, solve the equation step-by-step:
35 + 8n - 8 > 180
27 + 8n > 180
8n > 180 - 27
8n > 153
n > 153/8
n > 19.125
Since 'n' represents the number of days, it must be a whole number. So, we round up the decimal to the nearest whole number.
n > 20
Therefore, Annie completes the fitness program on the 21st day.
Note: We do not need to round the answer to a whole number in the starting calculation. It is okay to have a decimal value in the intermediate steps, but for practical purposes, we round it to a whole number at the end since the number of days cannot be a decimal.
In this case, it seems that rounding was necessary to get a whole number as an answer. The equation 180 = 27 + 8n represents the total amount of time Annie walked for the entire program (180 minutes), where n is the number of days she walked.
To solve the equation, you can isolate the variable n by subtracting 27 from both sides of the equation:
180 - 27 = 8n
153 = 8n
Then, divide both sides by 8 to solve for n:
153 / 8 = n
n ≈ 19.125
Since it's not possible to have a fraction of a day, rounding the answer to the nearest whole number gives us n = 20.
Therefore, Annie completes the fitness program on the 20th day.