Answer: the rate of the boat in calm water is 9 mph and the rate of the current is 5 mph
Step-by-step explanation:
Let x represent the rate of the boat in calm water.
Let y represent the rate of the current.
The woman paddling a canoe downstream with the river current travels 28 miles in 2 hours. Assuming that she paddled in the direction of the current, her total speed would be x + y mph
Distance = speed × time
Distance covered downstream is
28 = 2(x + y)
14 = x + y - - - - - - - - - - - -1
On the return trip, she paddles the same distance upstream against the river current in 7 hours.
Assuming that she paddled against the direction of the current, her total speed would be x - y mph
Distance = speed × time
Distance covered upstream is
28 = 7(x - y)
4 = x - y - - - - - - - - - - - -2
Adding equation 1 and equation 2, it becomes
18 = 2x
x = 18/2 = 9 mph
Substituting x = 9 into equation 1, it becomes
14 = 9 + y
y = 14 - 9 = 5 mph
;
= (2x+1)(x+2).