Answer: the boat can travel 20 mph in still water.
Explanation:
Let x represent the speed of the boat in still water.
Let y represent the speed of the current.
Distance = speed × time
Williams uses his small motorboat to go 5 miles upstream to his favorite fishing spot. Against the current, the trip takes 1/3 hour. The total speed would be (x - y) mph. The distance covered upstream is
5 = 1/3(x - y)
Cross multiplying by 3, it becomes
15 = x - y - - - - - - - - - - - -1
With the current the trip takes 1/5 hour. The total speed would be
(x + y) mph. The distance covered downstream is
5 = 1/5(x + y)
Cross multiplying by 5, it becomes
25 = x + y - - - - - - - - - - - -2
Adding equation 1 to equation 2, it becomes
40 = 2x
x = 20/2 = 20
Substituting x = 20 into equation 1, it becomes
15 = 20 - y
y = 20 - 15
y = 5