Two hikers, Alan and Ben, are 12.9 miles apart and walking towards each other. They meet in 3 hours. Find the rate of each hiker if Ben walks $0.5 \mathrm{mph}$ faster than Alan. Alan's rate of speed is $\mathrm{mph}$. (Round to one decimal place.) Ben's rate of speed is $\mathrm{mph}$. (Round to one decimal place.)

Step 1 ：Let's denote the speed of Alan as A mph and the speed of Ben as B mph. According to the problem, we know that \(B = A + 0.5\) mph.

Step 2 ：Since they are walking towards each other, their combined speed is \(A + B\) mph. They meet in 3 hours, so the total distance they covered is \((A + B) * 3\) miles.

Step 3 ：We know that the total distance is 12.9 miles, so we can set up the equation: \((A + B) * 3 = 12.9\).

Step 4 ：Substitute \(B = A + 0.5\) into the equation: \((A + A + 0.5) * 3 = 12.9\).

Step 5 ：Simplify the equation to: \(2A + 0.5 = 12.9 / 3\).

Step 6 ：Further simplify the equation to: \(2A + 0.5 = 4.3\).

Step 7 ：Solve for A: \(2A = 4.3 - 0.5\).

Step 8 ：Simplify to: \(2A = 3.8\).

Step 9 ：Solve for A: \(A = 3.8 / 2\).

Step 10 ：Simplify to: \(A = 1.9\) mph.

Step 11 ：Substitute \(A = 1.9\) into \(B = A + 0.5\): \(B = 1.9 + 0.5\).

Step 12 ：Simplify to: \(B = 2.4\) mph.

Step 13 ：So, Alan's rate of speed is \(\boxed{1.9}\) mph and Ben's rate of speed is \(\boxed{2.4}\) mph.