Question

Kellen's boat travels 12 mph. Find the rate of the
river current if she can travel 6 mi upstream in
the same amount of time she can go 10 mi
downstream. (Let x = the rate of the current.)
The rate of the river current is

Answer 1

Answer:

Rate of  river current is = 3 mph

Explanation:

Given speed of boat in still water is equal to 12mph

We know speed = distance divided by time

Given distance travelled upstream = 6 miles and

that  distance travelled downstream = 10 miles

Let x = rate of river current

and t = time taken to travel 6miles upstream as well as to travel 10 miles downstream

We know, speed downstream = speed of current + speed of boat = x + 12

Speed upstream = speed of current - speed of boat = x - 12

speed downstream = 10 divided by t and speed upstream = 6 divided by t  

so the two equations are -  

$\frac{10}{t}=\mathrm{x}+12$

and $\frac{6}{t}=x-12$

dividing the two equations we get  $\frac{10}{6}=\frac{(x+12)}{(x-12)}$

$10 \times(\mathrm{x}-12)=6 \times(\mathrm{x}+12)$

solving for x we get x = 3mph  is the rate of river current.