it takes julian 1/2 hours to walk 2 miles. he decides to start walking in his spare time, but because he wants to make sure he has enough time to go a desired distance he created a data table. at which ratio dose the consant of proportionality appear?
The constant of proportionality appears when there is a direct relationship between two variables. In this case, the ratio would be the time (in hours) it takes Julian to walk a certain distance.
To find the ratio for the constant of proportionality, we can set up a table:
Distance (in miles) | Time (in hours)
------------------------------------------
0.5 | 1/4
1 | 1/2
1.5 | 3/4
2 | 1
The ratio for the constant of proportionality is 1/2. This means that for every 1 mile Julian walks, it takes him 1/2 hour.
To determine the ratio at which the constant of proportionality appears in Julian's data table, we need to understand what the constant of proportionality represents in this scenario.
In Julian's case, the constant of proportionality represents the relationship between the time he spends walking and the distance he covers. This indicates how much time it takes him to cover each unit of distance.
As we know, it takes Julian 1/2 hour to walk 2 miles. This gives us the following ratio:
Time (hours) : Distance (miles) = 1/2 : 2
To find the constant of proportionality, we can simplify this ratio by multiplying both sides by 2 (to eliminate the denominator) and then multiplying both sides by 2 again (to make the time value a whole number):
1/2 * 2/1 = 2/2 = 1
So, the simplified ratio is:
Time (hours) : Distance (miles) = 1 : 2
The ratio 1 : 2 represents the constant of proportionality in Julian's case. It indicates that it takes him 1 hour to walk 2 miles, and this ratio remains constant regardless of the distance he wants to cover.
To find the ratio at which the constant of proportionality appears in Julian's data table, we need to analyze the relationship between the time and distance.
Given that Julian takes 1/2 hours to walk 2 miles, we can write this as a proportion:
1/2 hour / 2 miles = x hours / d miles
where x represents the time Julian takes to walk a desired distance, and d represents the desired distance.
Simplifying the proportion, we can cross-multiply:
(1/2) * d = 2 * x
d/2 = 2x
Dividing both sides by 2, we get:
d/4 = x
From this equation, we can see that the ratio between the desired distance (d) and the time taken by Julian (x) is 1:4, which means the constant of proportionality is 1/4.
it takes julian 1/2 hours to walk 2 miles. he decides to start walking in his spare time, but because he wants to make sure he has enough time to go a desired distance he created a data table. at which ratio dose the consant of proportionality appear?
hours miles walked
1/4 1
1/2 2
3/4 3
1 4
To determine the ratio at which the constant of proportionality appears in Julian's data table, we need to compare the relationship between the hours and the miles walked.
Looking at the data table:
Hours | Miles Walked
----------------------
1/4 | 1
1/2 | 2
3/4 | 3
1 | 4
We can compare the ratio of hours to miles walked using any two consecutive data points. Let's consider the first two data points (1/4 hour to walk 1 mile, and 1/2 hour to walk 2 miles).
The ratio between the hours and miles walked is:
(1/4 hour) / (1 mile) = (1/2 hour) / (2 miles)
To simplify this ratio, we can multiply both sides by 2:
(2 * 1/4) / 1 = (2 * 1/2) / 2
1/2 = 1/2
So, the ratio at which the constant of proportionality appears in Julian's data table is 1/2. This means that for every 1 hour Julian walks, he covers a distance of 2 miles.
ruth can read 15 pages in 30 minutes. she decides to create a table to keep track of her progress. from the data provided, at what ratio is the constant of proportionality?
times (hours) | pages read
-----------------------------------
1/2 | 15
1 | 30
1 1/2 | 45
2 | 60
To determine the ratio at which the constant of proportionality appears in Ruth's data table, we need to analyze the relationship between the time (in hours) and the number of pages read.
Given that Ruth can read 15 pages in 30 minutes, we can write this as a proportion:
30 minutes / 15 pages = x hours / p pages
where x represents the time Ruth takes to read a desired number of pages, and p represents the desired number of pages.
Simplifying the proportion, we can cross-multiply:
30 * p = 15 * x
30p = 15x
Dividing both sides by 15, we get:
2p = x
From this equation, we can see that the ratio between the number of pages read (p) and the time taken by Ruth (x) is 2:1, which means the constant of proportionality is 2/1 or simply 2.