The excursion boat on the river takes 2½ hours to make the trip to a point 12 miles upstream and to return. If the rate at which the boat travels in still water is 5 times the rate of the river current, what is the rate of the current?

Which of the following equations can be used to solve for c, the rate of the current?

[12/(4c)] + [12/(6c)] = 2.5

this answer iss wrong

this answer is wrong

To solve this problem, we need to set up an equation that represents the given information. Let's break down the problem step by step.

Let's denote the rate at which the boat travels in still water as "b" and the rate of the river current as "c". The speed at which the boat travels upstream is (b - c) and the speed at which it travels downstream is (b + c).

We are given that the excursion boat takes 2½ hours to make the round trip, which means it takes 2½ hours to go upstream (12 miles) and the same amount of time to return.

1. First, we need to find the time it takes to go upstream. We can use the formula:

Time = Distance / Speed

The distance is 12 miles, and the speed is (b - c). So, the time taken to go upstream is:

12 / (b - c)

2. The same amount of time is taken to travel downstream, so the time taken to go downstream is also:

12 / (b + c)

3. The total time taken for the round trip is 2½ hours, which can be written as 2.5. So, we set up the equation:

12 / (b - c) + 12 / (b + c) = 2.5

Now that we have the equation, we can determine which of the following options can be used to solve for "c", the rate of the current. Please provide the options you have, and I'll help you choose the correct one.

rate of river --- x mph

rate of boat --- 5x mph

12/x + 12/(5x) = 2.5
times 5x
60 + 12 = 12.5x
x = 5.76

change x to c