Mr Connors drives his car 11 miles each day to and from work. Is this distance mr Connors drives commuting to work proportional to the number of days he works ? How do you know?
yes
the word "each" means that m = 11d
Well, if Mr. Connors were to start driving his car to work and suddenly end up in Alaska after a few days, then something is clearly off and not proportional! However, assuming he keeps going to the same workplace, the distance Mr. Connors drives is indeed proportional to the number of days he works. You see, proportionality means that as one variable increases, the other variable also increases or decreases in a consistent and predictable manner. In this case, if the number of days Mr. Connors works increases, then the total distance he drives also increases by 11 miles for each additional day. So, as long as Mr. Connors keeps working at the same place, his distance traveled is indeed proportional to the number of workdays.
To determine if the distance Mr. Connors drives commuting to work is proportional to the number of days he works, we need to compare the two values.
Proportionality implies that the distance driven is directly or linearly related to the number of days worked. In other words, as the number of days worked increases, the distance driven should also increase proportionally, and vice versa.
To confirm if this holds true, we can calculate the ratio of the distance driven to the number of days worked.
Let's assume Mr. Connors works for 'n' number of days:
Distance driven = 11 miles
Number of days worked = n
The ratio of distance to days would be:
Ratio = Distance driven / Number of days worked
= 11 miles / n
If this ratio remains constant for all values of 'n', then we can conclude that the distance Mr. Connors drives commuting to work is proportional to the number of days he works.
However, without additional information regarding Mr. Connors' actual behavior or any hypothetically mentioned patterns, we cannot definitively confirm proportionality or non-proportionality.
To determine if the distance Mr. Connors drives commuting to work is proportional to the number of days he works, we need to compare the two quantities and see if they exhibit a consistent relationship. In this case, we are comparing the distance he drives with the number of days he works.
First, let's establish the relationship between these two quantities. Let's denote:
- Distance driven by Mr. Connors each day as "D"
- Number of days Mr. Connors works as "N"
Now, we can create an equation to represent the relationship between these quantities:
Distance = D * Number of Days
D = 11 miles (Given)
Number of Days = N (Number of days he works)
Substituting the values, our equation becomes:
Distance = 11 * N
Now, let's consider the definition of "proportional." Two quantities are said to be proportional if they always maintain the same ratio. In other words, if the ratio of the distance to the number of days remains constant, regardless of the specific values of distance or number of days.
So, if the ratio D/N remains constant, the distance Mr. Connors drives commuting to work is proportional to the number of days he works.
To verify if this assumption holds, we need more information on Mr. Connors' commuting habits over different time periods or variations in his work schedule. Based on the given information alone, we cannot definitively state whether the distance driven is proportional to the number of days worked.