Answer:
[tex]\large \boxed{\text{6 mi/h}}[/tex]
Step-by-step explanation:
Let s = speed of current
Then 24 - s = speed of motorboat upstream
and 24 + s = speed of motorboat downstream
Distance = speed × time
[tex]\begin{array}{rcl}\text{Time} & = & \dfrac{\text{ distance}}{\text{speed}}\\\\4.0 & = & \dfrac{45}{24 - s} + \dfrac{45}{24 + s}\\\\4.0(24 + s)(24 - s) & = &45(24 + s) + 45(24 - s)\\4.0(576 - s^{2}) & = &1080+ 45s + 1080 - 45s\\576 - s^{2} & = & 2160\\576 - s^{2} & = & 540\\s^{2}& = &36\\s &=& \textbf{6 mi/h}\end{array}\\\text{The speed of the current is $\large \boxed{\textbf{6 mi/h}}$}[/tex]
Check:
[tex]\begin{array}{rcl}4.0 & = & \dfrac{45}{24 - 6} + \dfrac{45}{24 + 6}\\\\4.0 & = & \dfrac{45}{18} + \dfrac{45}{30}\\\\4.0 & = & 2.5 + 1.5\\4.0 & = & 4.0\\\end{array}[/tex]
OK.
