Hours Miles Walked

Question

1/4 1
1/2 2
3/4 3
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?

Answer 1

The constant of proportionality can be determined by finding the ratio between the miles walked and the time taken to walk those miles.

So, for each pair of values in the table, we need to find the ratio.

For the first pair (1/4 hour and 1 mile):
Ratio = 1 mile / (1/4) hour
= 1 mile * 4/1 hour
= 4 miles/hour

For the second pair (1/2 hour and 2 miles):
Ratio = 2 miles / (1/2) hour
= 2 miles * 2/1 hour
= 4 miles/hour

For the third pair (3/4 hour and 3 miles):
Ratio = 3 miles / (3/4) hour
= 3 miles * 4/3 hour
= 4 miles/hour

For the fourth pair (1 hour and 4 miles):
Ratio = 4 miles / (1/1) hour
= 4 miles * 1/1 hour
= 4 miles/hour

As we can see, the ratio between the miles walks and the time taken to walk those miles is always 4 miles/hour. Therefore, the constant of proportionality appears as 4 in this data table.