Answer:
4 hours
Step-by-step explanation:
Given that:
Initial height of red candle = 8 inches
Rate of burning of red candle = [tex]\frac{7}{10}\ inch/hr[/tex]
Initial height of blue candle = 6 inches
Rate of burning of blue candle = [tex]\frac{1}{5}\ inch/hr[/tex]
To find:
Time taken in hours such that both the candles have the same height.
Solution:
Let the time taken such that both the candles have the same height = [tex]t[/tex] hours
Height of red candle after [tex]t[/tex] hours = [tex](8 - \frac{7}{10}t) \ inches[/tex]
Height of blue candle after [tex]t[/tex] hours = [tex](6 - \frac{1}{5}t) \ inches[/tex]
Writing both the expressions as equal:
[tex]8-\dfrac{7}{10}t=6-\dfrac{1}{5}t\\\Rightarrow 8-6=\dfrac{7}{10}-\dfrac{1}{5}t\\\Rightarrow 2 = (\dfrac{7-2}{10})t\\\Rightarrow \dfrac{5t}{10}=2\\\Rightarrow t=4\ hours[/tex]
After 4 hours, height of both the candles will be same.
