A boat can travel at an average speed of 10 miles per hour in still water. Traveling with the current, it can travel 6 miles in the same amount of time it takes to travel 4 miles upstreamUse the ratio T= D/R to construct a rational equation that can be solved for x to find the speed of the current Whats the answer? Please answer as soon as possible...

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.