Question

Question #f28b6

Answer 1

The height of the candle after `6` hours, will be `4` in.

Explanation:

A candle is 10 in. tall after burning for 2 hours. After 3 hours, it is 8.5 in. tall. How tall will the candle be after 6 hours?

We can make a linear equation to model the situation. Since time is the independent variable and height is the dependent variable, we can let `(x,y)` be `("time", "height")`, therefore the question gives us the points `(2,10)` and `(3,8.5)`, which we can use to find the slope, m:

`m=(10-8.5)/(2-3)=-1.5/1=-3/2`

Consider point-slope form:
`(y-y_1)=m(x-x_1)`
where `m` is the slope of the line and `(x_1,y_1)` is a point of the line.

Now, we can write a linear equation using point-slope form:
`y-10=-3/2(x-2)`

Since we want to know the height of the candle after 6 hours, we simply plug `x=6` into the above equation and solve for `y`:
`y-10=-3/2(6-2)`
`y=-3/2(4)+10`
`y=-6+10`
`y=4`

Therefore, the height of the candle after `6` hours, will be `4` in.

Answer 2

In support of the solution submitted by 'Y'

4 inches

Explanation:

Sometimes it is a good idea to 'scribble' a quick sketch to assist in visualisation of what the question is asking.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let the required height be `h`

What the target is:

Reference height - `x` = h

where `x` = burn rate x 4 hours
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Determine the burn rate")`

`("EB-EC inches")/("3-2 hours") -> (10-8.5)/(3-2) =1.5/1=3/2`

`" "3/2` inches in 1 hour

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine "x)`

`x=3/2 ("inches")/("hour")xx 4" hours"`

`x=3/(cancel(2)^1)xxcancel(4)^2" "("inches")/(cancel("hour"))xx cancel(" hours")`
`" "color(red)( uarr)`
`color(red)("manipulating units the same way as numbers")`

`x=3xx2" inches "=" "6" inches"`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine "h)`

`h=10 -x" inches "=" "10-6" "=" "4" inches"`