Answer:
Step-by-step explanation:
The speed of the cruiser in the direction of the current would be [tex](x + y) \; \rm mph[/tex]. Since the ship travels [tex]12\; \rm mi[/tex] at that speed in [tex]1\; \rm h[/tex], [tex]1 \times (x + y) = 12[/tex].
The speed of the cruiser in the opposite direction of the current would be [tex](x - y) \; \rm m \cdot s^{-1}[/tex]. Since the ship travels [tex]12 \; \rm mi[/tex] at that speed in [tex]2\; \rm h[/tex], [tex]2 \times (x - y) = 12[/tex].
Hence the system of equations:
[tex]\displaystyle \begin{cases}x + y = 12 \\ 2(x - y) = 12 \end{cases}[/tex].
Divide both sides of the second equation by [tex]2[/tex] to obtain:
[tex]x - y = 6[/tex].
Add that to the first equation:
[tex]2\; x = 18[/tex].
Hence [tex]x = 9[/tex].
Calculate [tex]y[/tex] using the first equation:
[tex]y = 12 - x = 12 - 9 = 3[/tex].
Hence:
