A motorboat travels 168 kilometers in 4 hours going upstream. It travels 280 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current

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