Question

Ratios and rates: complete a table and make a graph 622 Diggy's Doggy Day Care uses volunteers to play with the dogs. For every 10 minutes the volunteers and dogs play outside, they play for 20 minutes inside. Complete the table. Minutes outside 10 20 30 40 Minutes inside 20 Graph the data from the table. 200 180 160 140

Answer 1

We have a proportional relationship: for every 10 minutes outside, we have 20 minutes inside of playing.

Then, if "In" is the number of minutes inside and "Out" is the number of minutes outside, we can write:

`\text{In}=k\cdot\text{Out}`

The constant of proportionality k can be calculated from the fact that for every 10 minutes outside, we have 20 minutes inside of playing.

This means that when Out=10, In=20, so we have:

`k=\frac{\text{In}}{\text{Out}}=(20)/(10)=2`

Then:

`\text{In}=2\cdot\text{Out}`

This can be read as "the number of minutes inside is 2 times the number of minutes outside".

Then, we can complete the table:

Minutes outside: 10 20 30 40

Minutes inside: 20 40 60 80