A boat travels down a river for 2 h (traveling with the current), then turns around and takes 4 h to return (traveling against the current.) Let b be the rate of the boat, in miles per hour, in calm water and c be the rate of the current, in miles per hour. Suppose the distance traveled down the river by the boat is 24 mi. Write a system of equations that can be solved to find the rate of the boat in calm water and the rate of the current.

downstream:

speed = b+c

b+c = 24/2

=> b+c = 12

upstream:

speed = b-c

b-c = 24/4

=> b-c = 6

adding both eqyations:

=> 2b = 18

=> b = 9miles/hr

=> c = 3 miles/hr

rate of baot in calm water = 9 miles/hr

rate of current = 3 miles/hr