The correct answer is:
6 mph.
Explanation:
We will use the formula d = rt for this, where d is distance, r is rate, and t is time.
We know that the time for both distances is the same; this means we want to isolate t in our formula. To do this, we will cancel r by dividing both sides:
d/r = rt/r
d/r = t
We will write an expression for the time upstream, an expression for the time downstream, and set them equal.
For the time upstream, the distance is 6 and the rate is 24-x; this gives us
[tex]\frac{6}{24-x}[/tex]
For the time downstream, the distance is 10 and the rate is 24+x; this gives us
[tex]\frac{10}{24+x}[/tex]
Together, these give us the equation
[tex]\frac{6}{24-x}=\frac{10}{24+x}[/tex]
We cross-multiply to solve this:
6(24+x) = 10(24-x)
Using the distributive property, we have
6*24 + 6*x = 10*24 - 10*x
144+6x = 240-10x
Adding 10x to each side,
144+6x+10x = 240-10x+10x
144+16x = 240
Subtract 144 from each side:
144+16x-144 = 240-144
16x = 96
Divide both sides by 16:
16x/16 = 96/16
x = 6
