It takes a ship 4 hours to sail 420km 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 call the speed of the ship in still water "s" and the speed of the current "c".
When the ship is sailing with the current, it's easier to move, so the effective speed is s + c. We know that it sailed 420km in 4 hours, so we can set up an equation:
420 = (s + c) * 4
Similarly, when the ship is sailing against the current, it's harder to move, so the effective speed is s - c. We know that it sailed the same distance of 420km, but this time it took 6 hours:
420 = (s - c) * 6
Now we have two equations with two unknowns. We can solve for one of the variables, by isolating it in one equation and substituting it into the other. For example, we can isolate "s" in the first equation:
s + c = 420/4
s + c = 105
s = 105 - c
Now we substitute this expression for "s" into the second equation:
420 = (s - c) * 6
420 = (105 - c - c) * 6
420 = (105 - 2c) * 6
Dividing both sides by 6:
70 = 105 - 2c
2c = 35
c = 17.5
So the speed of the current is 17.5 km/h. To find the speed of the ship in still water, we can substitute this value back into either equation:
s + c = 105
s + 17.5 = 105
s = 87.5
So the speed of the ship in still water is 87.5 km/h.