Answer:
12 miles per hour
Step-by-step explanation:
Let speed of boat in still water be "x"
and speed of current be "c"
So, downstream rate would be "x + c"
And, upstream rate would be "x - c"
Now, given c = 4
We can use the distance formula, D = RT, where
D is distance, R is rate, and T is time
to solve this.
Downstream:
D = RT
92 = (x+4)(t)
Upstream:
D = RT
46 = (x-4)(t)
Both the times are same, we can equate both the times. Lets simplify first:
t = 92/(x+4)
and
t = 46/(x-4)
Equate:
[tex]\frac{92}{x+4}=\frac{46}{x-4}[/tex]
Now, cross multiply and solve for x to get our answer:
[tex]\frac{92}{x+4}=\frac{46}{x-4}\\92(x-4)=46(x+4)\\92x-368=46x+184\\46x=552\\x=12[/tex]
Speed of Boat (in still water) = 12 mph
