Amotorboat travels 180 km in 3 hours going upstream and 504 in 6 hours going downstream. what is the rate of the boat in still water and what is the rate of the current?

Speed of boat x = 84 km/hr

Speed of current = 12 km/hr

Step-by-step explanation:

Let 'x' be the speed of boat  and 'y' be the speed of still water

Upstream speed = x - y  and

Downstream speed = x + y

It is given that, A motorboat travels 180 km in 3 hours going upstream and 504 in 6 hours going downstream

Upstream speed = x - y = 180/3 = 60 km/hr

Downstream speed = x + y =  504/6 = 84 km/hr

To find the value of x and y

x + y = 84  (1)

x - y = 60   (2)

(1) + (2) ⇒

x + y = 84  (1)

x - y = 60  (2)

2x  + 0  = 144

x = 144/2 = 72

x + y = 84

y = 84 - 72 = 12

Therefore speed of boat x = 84 km/hr

Speed of current = 12 km/hr