Answer: The speed of the current is 2 miles per hour.
Step-by-step explanation:
We know that the speed of the boat is:
S = 10 mph.
When the boat travels with the current, the speed will be:
S = 10mph + x
where x = speed of the current.
When the boat travels against the current, the speed will be:
S = 10mph - x
Now, for a given amount of time T, when the boat travels with the current, it moves a distance of 6 miles.
Then we have the equation:
(10mph + x)*T = 6mi
And against the current, in the same time the boat moves 4 mi, then:
(10 mph - x)*T = 4mi
Then we have the system of equations:
(10mph + x)*T = 6mi
(10 mph - x)*T = 4mi
Now, we can take the quotient of these two equations and get:
((10mph + x)*T)/((10 mph - x)*T) = (6mi/4mi)
(10mph + x)/(10 mph - x) = 3/2
Now we can solve this for x.
(10mph + x) = (3/2)*(10 mph - x)
10mph + x = (3/2)*10mph - (3/2)*x
x + (3/2)*x = (3/2)*10mph - 10mph
(5/2)*x = (1/2)*10mph = 5mph
x = (2/5)*5mph = 2mph.
The speed of the current is 2 miles per hour.
