Atwelve inch candle and an 18 inch candle are lit at 6pm. the 12-in. candle burns 1.5 inches every hour. the 18 inch candle burns three inches every hour. at what time will the two candles be the same height?

at 10 PM

Step-by-step explanation:

A 12 inch candle and an 18 inch candle are lit at 6 PM.

The 12 inch candle burns 1.5 inches every hour.

The 18 inch candle burns 3 inches every hour.

Let h represents hour.

The height of 12 inch candle burns after h hours = 12 - 1.5h

The height of 18 inch candle burns after h hours = 18 - 3h

Both candles will be the same height

       18 - 3h = 12 - 1.5h

          1.5h  = 18 - 12

          1.5h = 6

               h =

               h = 4

After 4 hours time would be = 6 Pm + 4 hours = 10 PM

At 10:00 PM the two candles be the same height.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is