If you run 3 miles everyday for 5 days, how many miles will you need to run on the sixth day in order to have run an average of 4 miles per day over 6 days? Solve this problem in two different ways, and explain your solutions.
6 * 4 = 24 miles
3 * 5 = 15 miles
24 - 15 = 9 miles on day 6
Well, let's tackle this problem with a dash of humor, shall we?
First way: The "Straightforward Runner"
To find out how many miles you will need to run on the sixth day, we can start by calculating the total miles you will have run in the first five days. Since you run 3 miles every day for 5 days, you've already covered a total of 3 x 5 = 15 miles.
Next, to achieve an average of 4 miles per day over a total of 6 days, you'll need to run a total of 4 x 6 = 24 miles.
Now, to figure out how many miles you will need to run on the sixth day, just subtract the total miles you've already run from the target total. So, 24 - 15 = 9. Therefore, on the sixth day, you'll need to run 9 miles to have an average of 4 miles per day over 6 days.
Second way: The "Reverse Runner"
To spice things up, let's approach this problem from the other end. We know that our target average is 4 miles per day over 6 days, so the total distance we need to cover is 4 x 6 = 24 miles.
Now, since you've already run 15 miles in the first five days, you need to find out how many more miles you have left to reach the target. So, 24 - 15 = 9 miles. That means on the sixth day, you'll need to run 9 miles to achieve your desired average.
So, whether you prefer running in a straightforward manner or reversing your steps, the answer remains the same. On the sixth day, run like the wind and cover those 9 miles! Happy running!
Solution 1:
To find the total distance run over 6 days with an average of 4 miles per day, we multiply the average distance by the number of days. So, to run an average of 4 miles per day over 6 days, the total distance should be 4 miles/day * 6 days = 24 miles.
Now, let's consider the first 5 days, where the person runs 3 miles each day. The total distance covered in those 5 days is 3 miles/day * 5 days = 15 miles.
To find the distance needed to be run on the sixth day to achieve a total of 24 miles in 6 days, we subtract the total distance covered in the first 5 days from the target distance. So, the distance needed to be run on the sixth day is 24 miles - 15 miles = 9 miles.
Therefore, on the sixth day, the person needs to run 9 miles to achieve an average of 4 miles per day over 6 days.
Solution 2:
Using a different approach, we can understand that the total distance run over 6 days should be 6 miles/day * 4 days = 24 miles.
In the first 5 days, the person runs 3 miles each day, covering a total distance of 3 miles/day * 5 days = 15 miles.
To find the distance needed to be run on the sixth day, we again subtract the total distance covered in the first 5 days from the target distance. So, the distance needed to be run on the sixth day is 24 miles - 15 miles = 9 miles.
Hence, regardless of the approach used, running 9 miles on the sixth day will give a total of 24 miles in 6 days, with an average of 4 miles per day.
To solve this problem, let's consider two different approaches:
Approach 1:
Step 1: Calculate the total distance covered in 5 days by multiplying the distance per day (3 miles) by the number of days (5): 3 miles/day * 5 days = 15 miles.
Step 2: Calculate the total distance desired over 6 days by multiplying the average distance per day (4 miles) by the number of days (6): 4 miles/day * 6 days = 24 miles.
Step 3: Calculate the distance needed to run on the sixth day to achieve the desired average by subtracting the total distance covered in 5 days from the total desired distance over 6 days: 24 miles - 15 miles = 9 miles.
Therefore, you would need to run 9 miles on the sixth day to have run an average of 4 miles/day over 6 days.
Approach 2:
Step 1: Calculate the total distance covered in 5 days by multiplying the distance per day (3 miles) by the number of days (5): 3 miles/day * 5 days = 15 miles.
Step 2: Calculate the total distance desired over 6 days by multiplying the average distance per day (4 miles) by the number of days (6): 4 miles/day * 6 days = 24 miles.
Step 3: Subtract the total distance covered in 5 days from the total desired distance over 6 days to find the remaining distance needed to achieve the desired average: 24 miles - 15 miles = 9 miles.
Step 4: Divide the remaining distance needed by the number of remaining days (1) to find the distance needed to run on the sixth day: 9 miles / 1 day = 9 miles.
Therefore, using both approaches, you would need to run 9 miles on the sixth day to have run an average of 4 miles/day over 6 days.