Please Help.

[HappyDough]

Hi, I'm a middleschool student, and we're learning about rates/proportions. I have this math problem I've worked out but not quite gotten the answer. It's a griddable. The question is this:

School is 2 miles from home along a straight road. The table shows your distance from home as you walk home at a constant rate. Give the constant of proportionality as a decimal.

Time (min)	10	20	30
Distance from home (mi)	1.5	1	0.5

Then there's a grid like this:

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My work is similar to this:

k = y/x y=1.5 x=10 k = 1.5/10 k = 0.15
k = y/x y=1 x=20 k = 1/20 k = 0.05
k = y/x y=0.5 x=30 k = 0.5/30 k = 0.166666

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My problem is I can't find a constant of proportionality, as the numbers aren't, uh, constant. Or proportional. The "K" is different each time. I tried drawing up a graph but still, I couldn't figure it out. Any help is appreciated! Thanks.

Key:
Question
Regular Speech

 

[Ishuda]

The problem is the interpretation of 'constant of proportionality'. What that means in this case is that the rate is the same and the rate is the 'constant of proportionality'. So if you walk for an hour you will walk a distance of 4 times that if you walked for 15 min, that is distance is the rate times the time it took to walk that distance.

 

[HappyDough]

Thank you so much! I think I understand it now. Is the constant of proportionality (k) then 0.05?

 

[Ishuda]

Thank you so much! I think I understand it now. Is the constant of proportionality (k) then 0.05?

Yes.

As a point of information, it is sometimes useful to keep in mind just what units the constants (and variables) have. Sometime they can help you figure out a problem. For example k = 0.05 miles per minute. If you had been asked what is the proportionality constant in terms of miles per hour you would have
\(\displaystyle k = \frac{.05\space miles}{minute} = \frac{.05\space miles}{minute} * 1 = = \frac{.05\space miles}{minute} * \frac{60}{60} = \frac{60\space *\space .05\space miles}{60\space minute} = \frac{3\space miles}{hour}\)

 

[HappyDough]

Alright. Thanks again for your help!