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 7 hours against a river current of 4 km/ hr. On the way back, the same distance took him 5 hours with the same 4 km/hr current. Let r = Alvin's average paddling rate.

Answer 1

7 * (r - 4) = 5 * (r + 4) --> r = 24 km/h

Answer 2

Answer:

Alvin's average paddling rate = 24 km/hr

Step-by-step explanation:

Let r = Alvin's average paddling rate and s = distance of canoe trip.

On the way he is paddling against a river current of 4 km/ hr, so resultant rate of paddling is given by

                r' = r - 4

Time taken for on the way = 7 hours

So to cover s distance he takes 7 hours at a rate of r - 4.

                   s = 7 ( r - 4)

                   s = 7r - 28 ------------------------eqn 1

On the way back he is paddling in the direction of a river current of 4 km/ hr, so resultant rate of paddling is given by

                r' = r + 4        

Time taken for on the way back = 5 hours

So to cover s distance he takes 5 hours at a rate of r + 4.

                   s = 5 ( r + 4)  

                   s = 5r + 20 ------------------------eqn 2    

eqn 1 - eqn 2 gives

                    s -s = 7r - 28 - ( 5r + 20)

                       0 = 2r - 48

                        r =  24 km/hr        

Alvin's average paddling rate = 24 km/hr