A motorboat can go 14 miles downstream on a river in 20 mins. it takes 30 minutes for this boat to go back upstream the same 14 miles. find the rate of the boat in calm water an the rate of the current.

Answer: boat: 35 mph; current: 7 mphStep-by-step explanation:Let b and c represent the speeds of the boat and the current in miles per hour. Using the relationship ... distance/speed = timewe can write equations for the time going downstream and that going upstream. 14/(b+c) = 1/3 . . . . speeds add going downstream 14/(b-c) = 1/2 . . . . . current subtracts from boat speed going upstreamThese can be rearranged to the two linear equations ... b + c = 42 b - c = 28Adding the two equations gives ... 2b = 70 b = 35 . . . . . . divide by 2From the first equation, ... c = 42 -b = 42 -35 = 7The speed of the boat in calm water is 35 mph; the speed of the current is 7 mph.