Answer:
Therefore, the rate of the boat in still water is 8 mph and the distance between the towns is 30 miles.
Explanation:
We are given that the rate of the Mississippi River is 2 mph and it takes a boat 3 hours to travel downstream and 5 hours to travel upstream between the two towns. We need to find the rate of the boat in still water and the distance between the two towns.
To solve this problem, we can use the following system of equations:
rate downstream = rate in still water + rate of the river
rate upstream = rate in still water - rate of the river
Since the distance traveled downstream and upstream is the same, we can equate the two expressions for distance:
distance downstream = distance upstream
Substituting the expressions for rate from the first two equations into the third equation, we get:
(rate in still water + rate of the river) * time downstream = (rate in still water - rate of the river) * time upstream
We are given that the rate of the river is 2 mph, the time downstream is 3 hours, and the time upstream is 5 hours. Substituting these values into the equation, we get:
(rate in still water + 2) * 3 = (rate in still water - 2) * 5
Expanding both sides of the equation, we get:
3 * rate in still water + 6 = 5 * rate in still water - 10
Solving for the rate in still water, we get:
2 * rate in still water = 16
rate in still water = 8 mph
Now that we know the rate of the boat in still water, we can use either the downstream or upstream equation to find the distance between the two towns. Using the downstream equation, we get:
distance = (rate in still water + rate of the river) * time downstream
distance = (8 + 2) * 3
distance = 30 miles.