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

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 -

`(10)/(t)=\mathrm{x}+12`

and
`(6)/(t)=x-12`

dividing the two equations we get
`(10)/(6)=((x+12))/((x-12))`

`10 *(\mathrm{x}-12)=6 *(\mathrm{x}+12)`

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