Candle problem

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Gamer30

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Feb 23, 2022
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Hi everyone,
Recently, I have encountered the following maths problem:
"The height of the candle is 10cm. After 2 hrs, it was shorter by 2cm. So, what's the height of the candle 4 hrs later?"

Would greatly appreciate anyone who can share their solution to the above problem.
Thanks.
 
Gamer30 said:
Hi everyone,
Recently, I have encountered the following maths problem:
"The height of the candle is 10cm. After 2 hrs, it was shorter by 2cm. So, what's the height of the candle 4 hrs later?"

Would greatly appreciate anyone who can share their solution to the above problem.
Thanks.
Click to expand...
Do you know that the candle was burning at a constant rate?
Another question: "4 hours later" from what point? From time 0 or time 2?
 
AvgStudent said:
Do you know that the candle was burning at a constant rate?
Another question: "4 hours later" from what point? From time 0 or time 2?
Click to expand...
Thanks for pointing out. The candle was burning at 1cm/hr. Yup, I was referring to from time 0 (4hrs later).
 
Gamer30 said:
Sorry to say I'm not an expert in applying y=mx+b in this case. Therefore, would greatly appreciate someone who can show me the solution?
Click to expand...
But you ARE acquainted with the equation:

y = m * x + b

Do you know the definitions of the variables 'm' & 'b' in the equation written above?

If you do not know please Google the following term:

slope-intercept equation of a line​

You will find many videos explaining the terms. Please review some of those and come-back to tell us what you have learned about "m" & "b" and how you use those concepts for your problem.
 
Gamer30 said:
Sorry to say I'm not an expert in applying y=mx+b in this case. Therefore, would greatly appreciate someone who can show me the solution?
Click to expand...
Another way you can approach this problem is by making a table:
You know at time 0, the candle is 10. So after 1 hour, the candle height will be 9.
Time (hour)​
Candle Height (cm)​
010
19
3?
4?

After that, you can plot these coordinates, and connect the dots. You'll see the line y=mx+b. Hope this helps.
:)
 
Gamer30 said:
Hi everyone,
Recently, I have encountered the following maths problem:
"The height of the candle is 10cm. After 2 hrs, it was shorter by 2cm. So, what's the height of the candle 4 hrs later?"

Would greatly appreciate anyone who can share their solution to the above problem.
Thanks.
Click to expand...
Yet another way to think about it is like this: If in 2 hours it decreases by 2 cm, how much will it decrease in 4 hours? Then just subtract that amount.

It's very helpful if you tell us what you are learning, so we can aim our help at the appropriate level. You put this under arithmetic, not algebra, so we can guess that my way, or AvgStudent's way, may be what you are expected to do, but then many students don't pay attention to the category and it doesn't always tell us much.
 
Subhotosh Khan said:
But you ARE acquainted with the equation:

y = m * x + b

Do you know the definitions of the variables 'm' & 'b' in the equation written above?

If you do not know please Google the following term:

slope-intercept equation of a line​

You will find many videos explaining the terms. Please review some of those and come-back to tell us what you have learned about "m" & "b" and how you use those concepts for your problem.
Click to expand...
I understand that b is the y-intercept and m is the gradient of the equation but the main point is that HOW do i find the GRADIENT of the line y=m*x+b? Kindly reply here. Thanks.
 
Gamer30 said:
the main point is ...
HOW do i find the GRADIENT
Click to expand...
Hi Gamer30. When you know two pairs of (x,y) values, then the formula is:

\(\displaystyle \text{gradient} = \frac{y_2 - y_1}{x_2 - x_1}\)

Be careful to not mix up the order of those four values on the right-hand side, when substituting numerical values for those symbols.

Post #7 shows a table with two given (time,height) values -- that is to say (x,y) values. Use them in the gradient formula. It doesn't matter which pair of numbers you decide to call [imath](x_1,y_1)[/imath]. The other pair will then be [imath](x_2,y_2)[/imath].

Be mindful of signs, when you do the arithmetic. Cheers

:)

[imath]\;[/imath]
 
Otis said:
Hi Gamer30. When you know two pairs of (x,y) values, then the formula is:

\(\displaystyle \text{gradient} = \frac{y_2 - y_1}{x_2 - x_1}\)

Be careful to not mix up the order of those four values on the right-hand side, when substituting numerical values for those symbols.

Post #7 shows a table with two given (time,height) values -- that is to say (x,y) values. Use them in the gradient formula. It doesn't matter which pair of numbers you decide to call [imath](x_1,y_1)[/imath]. The other pair will then be [imath](x_2,y_2)[/imath].

Be mindful of signs, when you do the arithmetic. Cheers

:)

[imath]\;[/imath]
Click to expand...
Hi Otis, I know the gradient can be found in that way (as shown in the table form, #7 post) but is there OTHER way(s) to find it? (Just out of curiosity)
 
time = t increases by 1 hour and the height decreases by 1 cm. So the gradient = 1/-1=-1 = -1cm/1hr

Now, -1cm/1hr = -4cm/4hr so the height decreases 4cm in 4 hrs. 10cm-4cm = ?
 
Gamer30 said:
I know the gradient can be found [by formula] as shown in the table [in post #7], but is there [another way]
Click to expand...
Hi. The table in post #7 does not show the gradient (or its formula), so I'm not sure what you're thinking.

By the way, when you shouted "HOW" to find the gradient, you could have mentioned that you already knew the formula.

To answer your new question, I would say that sometimes given information allows us to see what the change in y is when the change in x is exactly 1. In those cases, the change in y is the gradient. But, that line of reasoning only works when the given numbers are "nice", like they are in your exercise.

If you don't understand what I mean or you're not familiar with thinking of gradient as the ratio 'rise over run', then let us know. Cheers :)

[imath]\;[/imath]
 
Otis said:
Hi. The table in post #7 does not show the gradient (or its formula), so I'm not sure what you're thinking.

By the way, when you shouted "HOW" to find the gradient, you could have mentioned that you already knew the formula.

To answer your new question, I would say that sometimes given information allows us to see what the change in y is when the change in x is exactly 1. In those cases, the change in y is the gradient. But, that line of reasoning only works when the given numbers are "nice", like they are in your exercise.

If you don't understand what I mean or you're not familiar with thinking of gradient as the ratio 'rise over run', then let us know. Cheers :)

[imath]\;[/imath]
Click to expand...
Hi Otis,
When I'm referring to table in post #7, I meant that I can use the values there to find the gradient. I understand the gradient formula but I was just wondering whether there is other simpler way(s) to find it. Sorry to mention that I learnt the gradient formula but application wise (rise over run), I still have a lot to learn from you all. Thanks for all the replies.
 
Gamer30 said:
just wondering whether there is other simpler way(s) to find it
Click to expand...
Oh, I didn't realize that you were asking for 'simpler' ways to find the slope. In this exercise, I'd say that realizing the slope from number sense is the simplest way (that is, from the given information: "after 2 hrs it was shorter by 2cm"). The rate is -1cm per hr, so m=-1.

You seem to have done that. :)

[imath]\;[/imath]
 
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