Answer:
The rate of the boat in still water is 48 km/h
The rate of current is 16 km/h
Step-by-step explanation:
Let the rate of the current be represented by c
Let the rate of the boat in still water be represented by r
The distance traveled by the boat, d = 128 km
Time taken by the boat to travel upstream, t₁ = 4 hours
The speed of the boat upstream, v₁ = d/t₁
The speed of the boat upstream, v₁ = 128/4
The speed of the boat upstream, v₁ = 32 km/h
Rate of the boat in still water - Rate of current = The speed of the boat upstream
r - c = v₁
r - c = 32...............................(1)
The time taken by the boat to travel downstream, t₂ = 2 hours
The speed of the boat downstream, v₂ = d/t₂
The speed of the boat downstream, v₂ = 128/2
The speed of the boat downstream, v₂ = 64 km/h
Rate of the boat in still water - Rate of current = The speed of the boat downstream
r + c = v₂
r + c = 64......................(2)
Subtract equation (1) from equation (2)
2c = 64 - 32
2c = 32
c = 32/2
c = 16 km/h
Substitute c = 16 into equation (1)
r - c = 32
r - 16 = 32
r = 32 + 16
r = 48 km/h
The rate of the boat in still water is 48 km/h
The rate of current is 16 km/h