Question

Question!!

The Garza family drives to a state park. The remaining distance, in miles, to reach the state park is 285−60x , where x represents the number of driving hours.

What does each part of the expression represent?

I am in assumption that 285 = the total distance of the trip. Then 60x represents the number miles driven over "x" hours. But what does 60 by itself represent??

Answer 1

I have left the choices of "the number of miles to drive each day" or "the number of miles to drive after 1 hour". There isn't any number assigned to how many hours are driven, so I don't think it it's this. But no where is it mentioned that there's more than one day to drive to the state park.

Answer 2

60 represents the miles.

`60x` means that it is the number of miles \(\bf\text{times}\) the number of driving hours.

When you say that it is `"miles driven over 'x' hours"`you are saying \(\large \frac{60}{x}\) (which is not the case).

Answer 3

But look at what I have left. I am confused, honestly.

Answer 4

What do you suppose that 285 represents? Look back to the problem for cues. What does x represent? In that case, what does 60 represent?

Answer 5

Look at your second response.

Answer 6

It surely correlates greatly with the third response.

Answer 7

Again, this question deals with the representation of quantities. Here you are dealing with distance, rate and time.

Answer 8

Now that you've pointed it out, @Vuriffy , it does.

Answer 9

The question never stated anything about days, but hours.

Answer 10

You are NOT asked to find any numerical answers.

Answer 11

No, yeah @mathmale that's why the answer with "1 hour" confused me.

Answer 12

You already know the total distance = 285 miles
Time = x driving hours
Rate (remember is always over 1) -- for example: 120 miles in 6 hours would be 20 miles per hour (or 20/1)

Answer 13

SOO!! Although there isn't any mention of how many hours are driven, the answer would with the mention of "1 hour", correct?

Answer 14

Yes! Do not assume anything extra if the problem didn't say it to you.

Answer 15

You have two answer choices left; which is the better response to the last question?

In response to the post by calculusxy: You have correctly identified what 285 and x represent. That leaves the "60." Think carefully: What could that possibly represent, if you're dealing with distance and time?

Answer 16

It surely wouldn't take a day to go 285 miles in my eyes.

Answer 17

In a vehicle, of course.

Answer 18

NO BUT WAIT!! In the second box, the expression I'm looking an answer for it 60x. 60x is the expression in which shows the number of miles driven after "x" hours, right?

Answer 19

Remember the speed is ___ miles PER hour. That's why you would have to multiply it by x (the # of driving hours).

Answer 20

@StarfireAndRobin Do you understand the approach?

Answer 21

I am understanding well enough. And now more so because of the comparison between minutes and miles....
So the "1 hour" response goes for the second box, and the "x hours" response to the third?

Answer 22

Wait, if 60 miles = 1 hour, then wouldn't the response "the number of miles driven after 1 hour" be the answer for the third box?

Answer 23

No!

I'll give an example:
For example X (a random person) drives 2 hours in the speed of 40 miles per hour. There's an expression which is \(40x\) where x represents the number of driving hours. Therefore, since 2 hours was driven you would do \(40(2)\) which equals to 80.

Answer 24

But your second response the 1 hour thing was correct

Answer 25

Which response? I'm loosing track of the chat, oops.

Answer 26

Think about this some more. Please note that "60 miles = 1 hour" is never true; it's similar to saying cat = dog.

Try using a different word to relate "number of miles driven" and "1 hour."

Answer 27

`SOO!! Although there isn't any mention of how many hours are driven, the answer would with the mention of "1 hour", correct?` - @StarfireAndRobin

Answer 28

Hint: 60 represents a "rate of change." Can you explain this?

" the answer would with the mention of "1 hour" " Please clarify your meaning. ???

Answer 29

I have to go now :) I hope I have helped you a little bit at least @StarfireAndRobin

Answer 30

Consider this:\[miles - (\frac{ miles }{ hour })(hours)\]

Answer 31

Compare this to the problem at hand. What can you learn from this expression?

Answer 32

With any value of miles and hours corresponding it would result to 0?

Answer 33

"It may not be completely accurate to state, depending on your speed, but I just used the assumption of "60 miles per hour" = 1 mile per minute." The speed has nothing to do with this. "60 mph" is always equal to "1 mile per minute." How will this help with the problem solution?

Answer 34

@StarfireAndRobin: Time for you to get re-involved here.

Answer 35

No, yes, of course. I was just reading the messages and deciding what to do.

Answer 36

It was a complete assumption, I was not completely agreeing with what I said anyways.

Answer 37

I'm a bit confused with the expression @mathmale gave out and how to compare it to my problem.

Answer 38

@calculusxy you have helped today, thank you!

Answer 39

Not sure completely, but I tried various miles and hours and I kept getting 0.

Answer 40

60 miles - 60miles/(2) * 2 = 60 - 30/1*2/1
= 60 - 60 = 0.

Answer 41

Would this be in the correct order, then? @mathmale @Vuriffy

Answer 42

Yes.

Answer 43

Alright, this is what I'm sticking with. Thank you all @Vuriffy @mathmale @calculusxy you have helped me greatly!!

Answer 44

I think I understand how the equation relates to where the choices go to. Good job! @StarfireAndRobin

Answer 45

I will definitely come back to tell whether or not it was correct.