2 employees and 3 trainees together can finish a project in 7 days, 6 employees and 13 trainees together can finish the same project in 2 days. Find the time taken by 4 employees and 4 trainees together to finish the same work.

Let e be one employee's daily work and t be one trainee's daily work. From first condition: 2e + 3t = 1/7. From second condition: 6e + 13t = 1/2. Subtracting 3×(first equation) from second: 4t = 1/2 - 3/7 = 1/14, so t = 1/56. Then 2e = 1/7 - 3/56 = 5/56, so e = 5/112. For 4 employees and 4 trainees: daily work = 4×(5/112) + 4×(1/56) = 20/112 + 4/56 = 20/112 + 8/112 = 28/112 = 1/4. Therefore 4 days needed.