A motorboat travels 385 kilometers in 7 hours going upstream and 420 kilometers in 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Let x = the rate in still water and y = the rate of the current.

Distance = rate x time

Set up two equations:

Upstream: 7(x-y) = 385

Simplify by dividing both sides by 7:

x-y = 55

Downstream 4(x+y) = 420

Simplify by dividing both sides by 4:

x + y = 105

Now add both equations together:

x - y = 55

x +y = 105

= 2x = 160

Divide both sides by 2:

x = 80

The rate is 80 km per hour in still water.

Now solve for Y, which is the current:

x- y = 55

Replace x with 80:

80-y = 55

y = 25 km/hr ( cuurent rate)

36 is the final answer! : )

37

step-by-step explanation: