Relative Motion - River/Boat problem

[Kosmos77]

Homework Statement

A boat takes 2.80 hours to travel 30.0 km down a river, then 4.50 hours to return. How fast is the river flowing

Homework Equations

Vac = Vab + Vbc

The Attempt at a Solution

I wasn't quite sure how to use the formula that the professor gave us which is above for this particular problem. The way I see it, since the problem doesn't say their is a change in acceleration, I'm thinking the speed of the boat IS the speed of the river seeing as it is saying "down" a river... so I just took 30 / 2.8 which gives me the speed of the boat but... It's not the answer.

 

[americanforest]

There are a couple of steps involved here:

1. Set up two equations for the speed of the boat when it is going with and against the current.

2. Set up an equation in which you state that the distance traveled in both cases in exactly the same.

3. Find a relationship between the boat speed and the current speed using the above.

4. Use the fact that they give you the distance traveled to your advantage. With this, you can set up another equation relating the boat and current speed. With two equations and two unknowns, you can finish the problem.

 

[thomate1]

I would approach this problem by first defining the variables and their relationships. In this case, we have the distance traveled (30.0 km), the time taken to travel that distance (2.80 hours), and the speed of the boat (which we can calculate by dividing the distance by the time, giving us 10.71 km/h). We also have the return trip, which takes 4.50 hours.

Using the formula Vac = Vab + Vbc, we can determine the speed of the river by subtracting the speed of the boat from the total speed of the boat and river. In this case, since we are given the time and distance for the return trip, we can calculate the total speed of the boat and river (30 km/4.5 hours = 6.67 km/h). Subtracting the speed of the boat (10.71 km/h) from this total gives us a speed of 6.67 km/h for the river.

Therefore, the river is flowing at a speed of 6.67 km/h. This approach allows us to use the given information to solve for the unknown variable in a systematic and scientific manner.