Question

Find the rate of change for the situation.
You run 7 miles in one hour and 21 miles in three hours.

Answer 1

Rate of change=Change in distance/change in time

Answer 2

A. 3 miles per hour
B. 3 hours
C. 7 miles
D. 7 miles per hour

Answer 3

There's a bit of 'trick' in this question: without thinking, it'd be easy to conclude that you have to do two sets of calculations, whereas only one is necessary.

S-B: Which answer do YOU think is correct, and why? Please show your work.

Answer 4

umm im guessing 21 divided by 3 so the answer would be "7miles per hour"?

Answer 5

That's a wild guess. You choose to neglect 7 miles in one hour. That is a serious mistake. Look closely at the definition and try again.

Answer 6

lol im confused now :(

Answer 7

Let's analyze the wording of this problem:

1) We are told, right up front, that "you run 7 miles in one hour." What's your speed / rate?
\[\frac{ 7~miles }{ 1~hour }=7 mph\]

Answer 8

2) We are told, very redundantly, that "you run 21 miles in three hours." Again we express this as a rate, which has the form of a fraction:\[\frac{21~miles }{ 3~hours }=\frac{ 7~miles }{ 1~hour }=7~mph\]

Answer 9

So the problem gives you more information than you really need to solve it. Or, the problem gives you practice in simplifying fractions!!

So, what is your final answer to this problem? You'll need to use the phrase "rate of change."