A boat traveled 504 miles downstream and back. The trip downstream took 14 hours. The trip back took 21 hours. What is the speed of the boat in still water? What is the speed of the current?

The speed of the boat in still water is 30 mph, and the speed of the current is 6 mph.

Step-by-step explanation:

Let's say b is the speed of the boat in still water, and c is the speed of the current.

Distance = rate * time

Going downstream:

504 = (b + c) * 14

36 = b + c

Going upstream:

504 = (b - c) * 21

24 = b - c

Two equations, two variables. Solve with substitution or elimination. To use elimination, add the equations together.

60 = 2b

b = 30

Plug into any equation to find c.

36 = b + c

36 = 30 + c

c = 6

The speed of the boat in still water is 30 mph, and the speed of the current is 6 mph.