Answer: the speed of the boat in still water is 12 mph and the speed of the current is 9 mph.
Step-by-step explanation:
Let x represent the speed of the boat in still water.
Let y represent the speed of the current.
The boat travelled 252 miles downstream and the same distance upstream.
The trip downstream took 12 hours. Assuming the boat travelled with the wind when going downstream, the total speed would be (x + y) mph.
Distance = speed × time
The expression for distance travelled downstream is
252 = 12(x + y)
Dividing through by 12, it becomes
21 = x + y- - - - - - - - - - 1
The trip back took 84 hours. Assuming the boat travelled against the wind when going back(upstream), the total speed would be (x - y) mph.
The expression for distance travelled upstream is
252 = 84(x - y)
Dividing through by 84, it becomes
3 = x - y- - - - - - - - - - 2
Adding equation 1 to equation 2, it becomes
24 = 2x
x = 24/2
x = 12 mph
Substituting x = 12 into equation 1, it becomes
21 = 12 + y
y = 21 - 12
y = 9 mph
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