Question

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.

Answer 1

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