The rate of distance to time is a measure of how fast something is moving. In this case, the rate is measured in meters per minute. The higher the rate, the faster the object is moving.
The rates in rows 1, 3, 5, and 8 are all different because the object is moving at different speeds at those times. For example, in row 1, the object is moving at a rate of 6 m/min, but in row 5, the object is moving at a rate of 12 m/min.
The rates in rows 2, 6, and 7 are all the same because the object is moving at a constant speed of 60 m/min during those times.
To complete the table, we need to find the distance and time for each of the remaining rows. We can do this by using the ratios that are given in the table.
Distance
Row Distance Ratio
3 120 1:2
4 ? 2:3
5 ? 3:4
6 240 4:5
7 ? 5:6
8 ? 6:7
9 ? 7:8
10 ? 8:9
To find the distance for row 4, we multiply the distance in row 3 by the ratio 2:3.
Distance in row 4 = 120 *
= 80
To find the distance for row 5, we multiply the distance in row 4 by the ratio 3:4.
Distance in row 5 = 80 *
= 60
We can continue this process to find the distance for all of the remaining rows.
Time
Row Time Ratio
1 6 1:5
2 ? 2:4
3 ? 3:3
4 ? 4:2
5 ? 5:1
6 ? 6:1
To find the time for row 2, we multiply the time in row 1 by the ratio 2:4.
Time in row 2 = 6 *
= 3
To find the time for row 3, we multiply the time in row 2 by the ratio 3:3.
Time in row 3 = 3 *
= 3
We can continue this process to find the time for all of the remaining rows.
Completed table
Row Distance Time
1 6 6
2 12 3
3 120 3
4 80 4
5 60 5
6 240 6
7 320 7
8 360 8
9 400 9
10 440 10
Rates
To find the rates, we divide the distance by the time.
Row Distance Time Rate
1 6 6 1
2 12 3 4
3 120 3 40
4 80 4 20
5 60 5 12
6 240 6 40
7 320 7 45.7
8 360 8 45
9 400 9 44.4
10 440 10 44
The rates for the first 3 rows are not equivalent. However, the rates for the last 7 rows are equivalent. This means that the distance traveled per unit time is constant for the last 7 rows.