Let's use the variable v to represent the current speed and t to represent the length of time.
If the distance traveled when the boat is with the current is 276 miles, we have:
![\begin{gathered} distance=speed\cdot time\\ \\ 276=(44+v)\operatorname{\cdot}t\\ \\ t=(276)/(44+v) \end{gathered}]()
Then, when the boat is against the current, the distance is 252 miles, so:
![\begin{gathered} 252=(44-v)\operatorname{\cdot}t\\ \\ t=(252)/(44-v) \end{gathered}]()
Equating both values of t, we have:
![\begin{gathered} (276)/(44+v)=(252)/(44-v)\\ \\ 252\operatorname{\cdot}(44+v)=276\operatorname{\cdot}(44-v)\\ \\ 11088+252v=12144-276v\\ \\ 252v+276v=12144-11088\\ \\ 528=1056\\ \\ v=(1056)/(528)=2 \end{gathered}]()
Therefore the current speed is 2 mph.