Answer
$\text{Speed of Pamela =4 mph and River speed =1 mph}$
Work Step by Step
Let us consider that $V_{p}$ = speed of Pamela and $V_{r}$ = river speed
The time taken to swim downstream will be:
$T_{1} = \dfrac{15}{V_{p} + V_{r}}$
This implies that
$V_{p} + V_{r} = \dfrac{15}{3} = 5$ mph
The time taken to swim upstream will be:
$T_{1} = \frac{15}{V_{p} - V_{r}}$
This implies that $V_{p} - V_{r} = \dfrac{15}{5} = 3$ mph
$V_{p} + V_{r} = 5~~~~~~~(1)$
$V_{p} - V_{r} = 3~~~~~~~(2)$
We add the two equations (1) and (2) to obtain:
$2V_{p} =8\\ V_{p} = 4 \ mph$
Now, back-substitute the value above into Equation (1) to solve $V_{r} = 5-4=1 \ mph$
Therefore, our desired results are:
$\text{Speed of Pamela =4 mph and River speed =1 mph}$
