Answer:
The speed of the boat is 56 km/hr
The rate of the current is 14 km/hr
Step-by-step explanation:
We are given the following;
- Distance traveled upstream = 168 km
- Time taken to travel upstream = 4 hours
- Distance traveled down stream = 280 km
- Time taken down stream = 4 hours
We are required to determine the speed of the boat in still water and the speed of the current.
We are going to take;
Speed of the boat as = x km/hr
Rate of flow of current = y km/hr
We can determine the speed of the boat upstream;
Speed = Distance ÷ time
= 168 km ÷ 4 hours
= 42 km/hr
But, the speed upstream is given by (x - y) km/hr
Therefore; ( x-y) km/hr = 42 km/hr ......................... Eqn 1
Speed of the boat down stream
speed = 280 km ÷ 4 hours
= 70 km/hr
But, the speed downstream is given by (x+y) km/hr
Therefore, x+y km/hr = 70 km/hr ........................... Eqn 2
Solving Eqn 1 and Eqn 2 simultaneously;
x - y = 42
x + y = 70
Eliminating x
-2y = - 28
y = 14 km/hr
Solving for x,
x = 42 + y
= 42 + 14
= 56 km/hr
Therefore, the speed of the boat is 56 km/hr while the rate of the current is 14 km/hr
