Julia paddleboat travels 2km/h in stilll water. The boat is paddled 4km down stream in the same time it takes to go 1km upstream what is the speed of the river.
Please help and show all work I suck at story problems haha
ha ha
if you can read, just put it into math. If the river's speed is x, then since time = distance/speed,
4/(2+x) = 1/(2-x)
No problem, I'm here to help you! Let's break down the problem step by step.
Let's assume the speed of the river is "x" km/h.
The speed of the boat in still water is given as 2 km/h, meaning if there was no current in the river, the boat would travel at a speed of 2 km/h.
When the boat is traveling downstream (going with the current), its effective speed will be the sum of the speed of the boat in still water and the speed of the river. So the speed of the boat downstream is (2 + x) km/h.
Similarly, when the boat is traveling upstream (going against the current), its effective speed will be the difference between the speed of the boat in still water and the speed of the river. So the speed of the boat upstream is (2 - x) km/h.
Now, let's consider the time taken to paddle 4 km downstream. We can use the formula Time = Distance / Speed.
Since Time is the same both upstream and downstream (as mentioned in the problem), we can equate the two time expressions:
4 km / (2 + x) km/h = 1 km / (2 - x) km/h
Cross-multiplying, we have:
4(2 - x) = 1(2 + x)
Simplifying further:
8 - 4x = 2 + x
Now, bring all the "x" terms to one side and the constant terms to the other side:
4x + x = 8 - 2
5x = 6
Divide both sides of the equation by 5:
x = 6/5
Therefore, the speed of the river is 6/5 km/h or 1.2 km/h.
To summarize:
The speed of the river is 1.2 km/h.