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 10 hours against a river current of 2k(m)/(h)r. On the way back, the same distance took him 6 hours with the same 2k(m)/(h)r current.

Answer 1

To calculate the average paddling rate, equations are set up based on the canoe's speed in still water, the river current speed, and the times taken in each direction. By solving these simultaneously, we can find the canoe's speed in still water and the average speed for the entire trip.

Step-by-step explanation:

To calculate Alvin's average paddling rate for his canoe trip, we need to consider the rates going to and coming from the campsite. Since the river current is working against him on the way there and with him on the way back, these effects will influence his paddling rate differently in each direction.

Let's define vars:

• v = canoe's speed in still water
• r = river current speed
• d = distance to the campsite
• t1 = time to get to the campsite
• t2 = time to get back

On the way there, the effective speed of the canoe is (v - r) because the current is against him. On the way back, the effective speed is (v + r) because the current is with him. We know:

• t1 = 10 hours
• t2 = 6 hours
• r = 2 km/h

Since the distance is the same both ways, we can write two equations:

1. d = (v - r) * t1
2. d = (v + r) * t2

Solving these equations simultaneously, we get:

• v = (d/t2 - r + d/t1 + r) / 2

We don't have the value of d, but we can solve for v in terms of d.

The average speed for the entire trip is the total distance divided by the total time, which is 2d / (t1 + t2).