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.
Accepted Solution
A:
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.