Person A leaves his home to visit his​ cousin, person​ B, who lives 243 miles away. He travels at an average rate of 46 miles per hour. One​ half-hour later, person B leaves her house to visit person​ A, traveling at an average rate of 64 miles per hour. How long after person B leaves will it be before they​ meet?

They meet (or pass) each other two hours after B leaves.

When B starts trip A has already gone 23 miles (46 x 0.5)
This means they are still 220 miles apart.
Their closing speed is 46 + 64 = 110 mph.
They will meet 2 hours after B leaves home. (220 / 110)

A will have travelled 46 x 2.5 = 115 miles and B will have travelled 2 x 64 = 128 miles