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There is NO such conception "speed of the boat", at all.
There is a conception "speed of the boat relative to something", instead.
In your case the question is about speed of the boat in still water.
Let x be the speed of the boat in still water.
Then the speed of the boat moving downstream is (x+7) mph;
moving upstream is (x-7) mph.
Write the "time" equation
=
Cross-multiply, simplify and find x
120*(x-7) = 105*(x+7)
8*(x-7) = 7*(x+7)
8x - 56 = 7x + 49
8x - 7x = 49 + 56
x = 105 mph, which is quite unrealistic.
You better throw this "problem" to the closest garbage bin.