Amotorboat 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.

boat: 35 mph; current: 7 mph

Step-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 = time

we 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 upstream

These can be rearranged to the two linear equations ...

b + c = 42

b - c = 28

Adding the two equations gives ...

2b = 70

b = 35 . . . . . . divide by 2

From the first equation, ...

c = 42 -b = 42 -35 = 7

The speed of the boat in calm water is 35 mph; the speed of the current is 7 mph.