1. Given:

   • First distance $d_1 = 4\text{ km}$ at speed $v_1 = 3\text{ km/h}$
   • Second distance $d_2 = 4\text{ km}$ at speed $v_2 = 5\text{ km/h}$

2. Average speed formula: $v_{\text{avg}} = \frac{\text{Total distance}}{\text{Total time}}$

3. Compute total distance: $d_{\text{total}} = 4 + 4 = 8\text{ km}$

4. Compute time for each part:

   • Time for first $4$ km: $t_1 = \frac{d_1}{v_1} = \frac{4}{3}\text{ h}$
   • Time for second $4$ km: $t_2 = \frac{d_2}{v_2} = \frac{4}{5}\text{ h}$

5. Total time: $t_{\text{total}} = \frac{4}{3} + \frac{4}{5} = \frac{20+12}{15} = \frac{32}{15}\text{ h}$

6. Average speed: $v_{\text{avg}} = \frac{8}{32/15} = 8 \times \frac{15}{32} = \frac{15}{4} = 3.75\text{ km/h}$

7. Check options:

   • A: $3.75\text{ km/h}$ ✔️
   • B: $4.25\text{ km/h}$ ✖️
   • C: $3.50\text{ km/h}$ ✖️
   • D: $4.00\text{ km/h}$ ✖️

Therefore, the correct answer is Option A.