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 3k(m)/(h)r. On the way back, the same distance took him 5 hours with the same 3k(m)/(h)r current.

Answer 1

To find Alvin's average paddling rate, set up equations representing the trips to and from the campsite. Upon solving these equations, we find that his average paddling rate in still water is 18 km/h.

Step-by-step explanation:

The question involves calculating the average paddling rate for a canoe trip taken by Alvin. To determine the rate, we consider both the trip against the current and with the current. When Alvin paddles against the current, his effective speed is reduced, whereas with the current, it's increased.

Given that the river current is 3 km/h and assuming Alvin's paddling rate in still water is constant, we can set up two equations to represent his trips to and from the campsite. The effective rate going to the campsite is (rate in still water - 3 km/h), and coming back is (rate in still water + 3 km/h).

Let r be the rate of Alvin's paddling in still water, then on the way to the campsite, his rate is r - 3 km/h, and it took him 7 hours. On the way back, his rate is r + 3 km/h, and it took him 5 hours. Because the distance is the same for both trips, we can express the distance as d = (r - 3) × 7 and d = (r + 3) × 5. Solving these equations for r will give us Alvin's average paddling rate in still water.

To solve for r, we set the two expressions for d equal to each other and simplify.

1. (r - 3) × 7 = (r + 3) × 5
2. 7r - 21 = 5r + 15
3. 2r = 36
4. r = 18 km/h

Thus, Alvin's average paddling rate in still water is 18 km/h.