Question

Mrs. Kudra's Algebra 2/Trig class went on a 50-mile (one way) canoe trip upstream and then back again in a total of 7 hours and 30 minutes. In still water, the speed at which they paddled was 15 miles per hour. What is the speed of the river's current?

Answer 1

To find the river's current speed, we use relative velocity concepts to set up two equations based on the upstream and downstream trip times. By solving these equations simultaneously with the canoe's still water speed and total time used for the trip, we can determine the river's current speed.

Step-by-step explanation:

To solve the problem of determining the speed of the river's current, we apply concepts of relative velocity. Let's denote the speed of the canoe in still water as Vcw and the speed of the river's current as Vr.

When moving upstream, the effective speed of the canoe is Vcw - Vr. Similarly, when moving downstream, the effective speed is Vcw + Vr. Given that the total trip is 100 miles (50 miles upstream and 50 miles downstream) and the time taken for the whole trip is 7.5 hours, we can write two equations reflecting the total time spent going upstream (Tu) and downstream (Td).

The equations are:
Tu = 50 / (Vcw - Vr)
Td = 50 / (Vcw + Vr)
Since Vcw is 15 mph and Tu + Td is 7.5 hours, we can solve these two equations simultaneously to find Vr, the speed of the river's current.