Question #f28b6

2 Answers
May 12, 2017

The height of the candle after 66 hours, will be 44 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)(x,y) be ("time", "height")(time,height), therefore the question gives us the points (2,10)(2,10) and (3,8.5)(3,8.5), which we can use to find the slope, m:

m=(10-8.5)/(2-3)=-1.5/1=-3/2m=108.523=1.51=32

Consider point-slope form:
(y-y_1)=m(x-x_1)(yy1)=m(xx1)
where mm is the slope of the line and (x_1,y_1)(x1,y1) is a point of the line.

Now, we can write a linear equation using point-slope form:
y-10=-3/2(x-2)y10=32(x2)

Since we want to know the height of the candle after 6 hours, we simply plug x=6x=6 into the above equation and solve for yy:
y-10=-3/2(6-2)y10=32(62)
y=-3/2(4)+10y=32(4)+10
y=-6+10y=6+10
y=4y=4

Therefore, the height of the candle after 66 hours, will be 44 in.

May 12, 2017

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.
Tony BTony B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let the required height be hh

What the target is:

Reference height - xx = h

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

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

("EB-EC inches")/("3-2 hours") -> (10-8.5)/(3-2) =1.5/1=3/2EB-EC inches3-2 hours108.532=1.51=32

" "3/2 32 inches in 1 hour

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

x=3/2 ("inches")/("hour")xx 4" hours"x=32incheshour×4 hours

x=3/(cancel(2)^1)xxcancel(4)^2" "("inches")/(cancel("hour"))xx cancel(" hours")x=321×42 incheshour× 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"