Alvin wants to know what his average paddling rate was for a canoe trip to a campsite. on the way there it took him 8 hours against a river current of 3 km/ hr. on the way back, the same distance took him 3 hours with the same 3 km/hr current. let r = alvin's average paddling rate.

let

r> Alvin's average paddling rate in km/hour

y > speed of the current in km/hour

we know that

speed= distance/time > solve for distance

distance=speed*time

to Campsite against the current

speed=r-y> speed=(r-3)

time=8 hours

distance=(r-3)*8> equation 2

From Campsite with the current

speed=r+y> speed=(r+3)

time=3 hours

distance=(r+3)*3> equation 1

equate equation 1 and equation 2> because is the same distance

(r+3)*3=(r-3)*8> 3r+9=8r-24> 8r-3r=24+9> 5r=33> r=6.6 km/hour

therefore

the answer is

Alvin's average paddling rate is 6.6 km/hour

she will travel a distance in the range of 3 - 11 miles