River Current Speed: 2m/s or 4m/s?

[Krystan]

Homework Statement

Shareen finds that when she drives her motorboat upstream she can travel with a speed of only 8m/s, while she moves with a speed of 12m/s when she heads downstream. What is the current of the river on which Shareen is traveling?

The Attempt at a Solution

x= current speed
b= boat speed

x+b= 12m/s
b-x= 8m/s
b=x+8
x+x+8= 12
2x= 4
x=2

12m/s-8m/s=4m/s

Our physics class is having a debate on whether the answer is 2m/s or 4m/s and why.

 

[krausr79]

I agree with your first answer, for reasons the algebra suggests. Maybe solve for the boat speed in either case? It will likely be inconsistent at 4m/s.

 

[thomate1]

I would say that the answer to this question is 2m/s. This is because the given information states that Shareen can travel with a speed of 8m/s upstream and 12m/s downstream. This means that the boat's speed (b) is equal to the current speed (x) plus 8m/s (b=x+8). Using this information, we can set up the equation 2x=4, where x represents the current speed. Solving for x, we get x=2m/s. This means that the current speed of the river on which Shareen is traveling is 2m/s.

It is important to note that the current speed and the boat's speed are not the same. The boat's speed is affected by the current, but it is not the same as the current speed. Therefore, we cannot simply subtract the upstream speed from the downstream speed to get the current speed. Instead, we must use the given information and set up an equation to solve for the current speed.

In conclusion, the current speed of the river on which Shareen is traveling is 2m/s. This answer is supported by the given information and the use of mathematical equations. It is important to carefully consider all given information and use scientific reasoning to arrive at a correct answer.