46 Weeks.
We could cross out 92 weeks and 184 as Both would be far from filled a tiny bit (empty). That leaves either 46 weeks or 2 weeks. Now let's try out 46 weeks. 46x3 is 138. So the water tank with 256 gallons will have 118 gallons left. Now 46x5 is 230. Subract that from 348. That gives 118 also. Which means at this point they both have 118 gallons (same amount).