Question

How Long will it take the candle to burn completely How do you know?

Answer 1

`\sf\\\textsf{The line given in the figure passes through (0, 9) and (4, 1).}\\\textsf{Using two point form,}\\\\y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)\\\\\textsf{this represents the equation of the line passing through }(x_1,y_1)\textsf{ and }(x_2,y_2).`

`\sf\\\textsf{So let }(x_1,y_1)=(0,9)\textsf{ and }(x_2,y_2)=(4,1).\\\textsf{Now,}\\\\y-9=(1-9)/(4-0)(x-0)\\\\\textsf{or, }y-9=-2(x-0)\\\textsf{or, }2x+y=9\textsf{ is the equation of the line shown in the graph.}`

`\sf\\\textsf{The graph represents height of the candle(h) as y-axis and time taken(t) as x-axis.}\\\textsf{So we may write the equation as:}\\2t+h=9`

`\textsf{Now according to the question we need to find the time taken for the candle to }\\\textsf{burn completely. This means, at that time, height of candle(h) = 0}`

`\sf\\\textsf{Putting h = 0 in the equation,}\\2t+0=9\\\textsf{or, }t=4.5`
`\textsf{This is the required time for the candle to burn completely.}`