A boat traveling on the Snake River travels 24 miles upstream in 3 hours. The return trip takes the boat only 2 hours. Find the rate of the boat in still water.
V1 = d/t = 24 / 3 = 8 mi/h.
V2 = 24 / 2 = 12 mi/h.
Vavg = (V1 + V2) / 2 = (8 + 12) / 2 = 10 mi/h = speed in still water.
To find the rate of the boat in still water, we can use the formula: rate in still water = (rate upstream + rate downstream) / 2.
Let's begin by finding the rate upstream:
Distance traveled upstream = 24 miles
Time taken upstream = 3 hours
Rate upstream = Distance traveled upstream / Time taken upstream = 24 miles / 3 hours = 8 miles per hour.
Next, let's find the rate downstream:
Distance traveled downstream = Distance traveled upstream (since it's a round trip) = 24 miles
Time taken downstream = 2 hours
Rate downstream = Distance traveled downstream / Time taken downstream = 24 miles / 2 hours = 12 miles per hour.
Now we can find the rate of the boat in still water:
Rate in still water = (rate upstream + rate downstream) / 2 = (8 miles per hour + 12 miles per hour) / 2 = 20 miles per hour / 2 = 10 miles per hour.
Therefore, the rate of the boat in still water is 10 miles per hour.