A blue candle and red candle are lit at the same time but burn at different rates. The blue candle is 7.4 inches long when lit and burns at a constant rate of 2.8 inches per hour. The red candle is 5.5 inches long when lit and burns at a constant rate of 1.1 inches per hour. a. For each candle, write a formula expressing the remaining length of the candle (in inches) in terms of the number of hours $\mathrm{t}$ since the candle was lit. Blue Candle: $l=$ Preview Red Candle: $l=$ Preview b. The time-length relationship for the two candles form a system. Find the solution(s) to this system. One solution: $(t, l)=$ Preview No solution Infinite number of solutions

Step 1 ：Let's denote the remaining length of the blue candle as \(l_b\) and the remaining length of the red candle as \(l_r\). The length of each candle decreases linearly with time, so we can express \(l_b\) and \(l_r\) as functions of time \(t\) (in hours) as follows:

Step 2 ：For the blue candle, \(l_b = 7.4 - 2.8t\)

Step 3 ：For the red candle, \(l_r = 5.5 - 1.1t\)

Step 4 ：We are asked to find the time \(t\) when the lengths of the two candles are equal. This means we need to solve the equation \(7.4 - 2.8t = 5.5 - 1.1t\) for \(t\).

Step 5 ：Solving the equation gives \(t \approx 1.12\) hours.

Step 6 ：Substituting \(t \approx 1.12\) into either of the two equations gives the length of the candles at this time as \(l \approx 4.14\) inches.

Step 7 ：\(\boxed{\text{Final Answer: The formulas expressing the remaining length of the candles in terms of the number of hours since the candle was lit are } l_b = 7.4 - 2.8t \text{ for the blue candle and } l_r = 5.5 - 1.1t \text{ for the red candle. The solution to the system formed by these two equations is approximately } (1.12, 4.14)\text{, meaning that after approximately 1.12 hours, both candles will be approximately 4.14 inches long.}}\)