Question

A candle is 7in tall after burning for 1 h. The same candle is 5 1/2 in y’all after burning for 4 h. How tall will the candle be after burning for 6 h

Answer 1

4.5 inch

Explanation:

Given: A candle is 7 inch tall after burning for 1 hour.

Same candle is 5.5 inch tall after burning for 4 hours.

Lets assume time to burn candle be "x" and height of candle be "y".

Now, finding the rate of changes in height of candle per hour.

Let "m" represent the changes in height of candle per hour.

we know,
`m= (Changes\ in\ length)/(Changes\ in\ time)`

∴ m=
`(5.5-7)/(4-1) = (-1.5)/(3)`

m=
`-0.5`

Next, forming an equation to know the original height of candle.

using equation;
`y= mx+ original\ height`

We know, A candle is 7 inch tall after burning for 1 hour.

⇒
`7= -0.5* 1+ original\ height`

⇒
`7= -0.5+ original\ height`

Adding both side by 0.5

⇒
`Original\ height= 7.5\ inches`

Hence, the original height of candle was 7.5 inches.

Again using the same equation to find the height of candle after burning for 6 hour.

`y= -0.5* 6+ 7.5`

⇒
`y= -3+7.5`

∴ y= 4.5 inches.

Hence, The candle will be 4.5 inches tall after burning for 6 hour.