It takes a ship 4 hours to cover 420 km with the current and 6 hours against the current. Find the speed of the ship in still water and the speed of the current.

Let s be the speed of the ship, and c be the speed of the current. 

We know that distance equals speed multiplied by the time. 

With the current
     [tex]\left(s+c\right)\left(4\:hours\right)=420\:km[/tex]
     or
     [tex]s+c=105[/tex]
This is our first equation.

Now, against the current, we have
     [tex]\left(s-c\right)\left(6\right)=420[/tex]
     or
     [tex]s-c=70[/tex]
This is our second equation. 

We solve the equations simultaneously, by adding them together
     [tex]2s-0c=175[/tex]

     [tex]s=87.5\:km/hr[/tex]

Substitute s=87.5 to the first equation to solve for c.
     [tex]87.5+c=105[/tex]

     [tex]c=17.5\:km/hr[/tex]

The speed of the ship is 87.5 km/hr and the speed of the current is 17.5 km/hr.