Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

Two tailors, Lara and Emma, sit down to do some embroidery. Lara can embroider 3 shirts per hour, and Emma can get through 4 shirts per hour. In addition, the tailors had previously finished some shirts. Lara has already completed 17 shirts, and Emma has completed 8 shirts. Lara and Emma decide to take a break when they have finished the same total number of shirts. How many shirts, in total, will each tailor have finished? How long will that take?

Each tailor will have finished a total of shirts in hours.
Submit

Step 1 ：Define the symbols L, E, and total_shirts to represent the number of hours Lara works, the number of hours Emma works, and the total number of shirts, respectively.

Step 2 ：Write the equation for Lara's work as \(3L + 17 = \text{total_shirts}\). This represents the fact that Lara can embroider 3 shirts per hour and has already completed 17 shirts.

Step 3 ：Write the equation for Emma's work as \(4E + 8 = \text{total_shirts}\). This represents the fact that Emma can embroider 4 shirts per hour and has already completed 8 shirts.

Step 4 ：Solve the first equation for L to get \(L = \frac{\text{total_shirts}}{3} - \frac{17}{3}\).

Step 5 ：Substitute the expression for L from the previous step into the second equation to get \(4E + 8 = 3(\frac{\text{total_shirts}}{3} - \frac{17}{3}) + 17\).

Step 6 ：Solve this equation for E to get \(E = \frac{\text{total_shirts}}{4} - 2\).

Step 7 ：Substitute the value of E into the first equation to find the total number of shirts, which gives \(\text{total_shirts} = 3L + 17\).

Step 8 ：Calculate the time it will take for each tailor to finish the same total number of shirts by dividing the total number of shirts by 3, which gives \(\text{time} = L + \frac{17}{3}\).

Step 9 ：Final Answer: Each tailor will have finished a total of \(\boxed{\text{total_shirts_value}}\) shirts in \(\boxed{\text{time}}\) hours.