Respuesta :
Answer: the rate of the boat in still water is 41 mph.
the rate of the current is 11 mph.
Step-by-step explanation:
Let x represent the rate of the boat in still water.
Let y represent the rate of the current.
A motorboat travels 210 miles in 7 hours going upstream. This means that the total speed with which the boat travelled is (x - y) mph.
Distance = speed × time
Distance travelled by the motor boat while going upstream is
210 = 7(x - y)
Dividing both sides of the equation by 7, it becomes
30 = x - y- - - - - - - - - - - 1
It travels 364 miles going down stream in the same amount of time. This means that the total speed with which the boat travelled is (x + y) mph.
Distance travelled by the motor boat while going downstream is is
364 = 7(x + y)
Dividing both sides of the equation by 7, it becomes
52 = x + y- - - - - - - - - - - 2
Adding equation 1 to equation 2, it becomes
82 = 2x
x = 82/2
x = 41
Substituting x = 41 into equation 2, it becomes
52 = 41 + y
y = 52 - 41
y = 11
