Answer:Rate of the boat in still water: 45 km/h
Rate of the current = 5 km/h
Step-by-step explanation:
Let x represent the rate of the boat in still water:
Let y represent the rate of the current
Recall,
Distance = speed x time
From the information given, the motorboat takes 5 hours to travel 200 kilometers going upstream. While moving upstream, the current opposes motion. Thus, total speed is x - y. It means that
200 = 5(x - y)
Dividing both sides by 5,
40 = x - y equation 1
The return trip takes 4 hours going downstream. While moving downstream, the current aids motion. Thus, total speed is x + y. Since the distance is the same, it means that
200 = 4(x + y)
Dividing both sides by 4,
50 = x + y equation 2
By adding equations 1 and 2, we have
40 + 50 = x + x - y + y
90 = 2x
x = 90/2
x = 45
Substituting x = 45 into equation 1, it becomes
40 = 45 - y
y = 45 - 40
y = 5
Rate of the boat in still water: 45 km/h
Rate of the current = 5 km/h