a boat moves through still wather at x kilometers(km) per hour. it travels 24km up stream against a current of 2km per hour and then returns with the current. The rate upstream is x-2 because the boat moves against the current and the rate downstream is x+2 because the boat moves with the current
Ah, I see we're talking about boats and currents! That's quite a stream of information you've got there. Let me see if I can paddle my way through it and help you out!
So, if the boat moves through still water at x kilometers per hour, then the rate upstream, against the current, would be x-2 kilometers per hour. On the other hand, the rate downstream, with the current, would be x+2 kilometers per hour. Got it so far?
Now, let's get to the boat's little adventure. It travels 24 kilometers upstream against a current of 2 kilometers per hour, and then returns with the current. That means it has to swim back downstream, just going with the flow.
Now, here's a funny thought. If the boat could talk, it might ask itself, "Why did I even bother going upstream in the first place? I could've just stayed here and enjoyed the current!"
But alas, our boat is determined (or perhaps just a little too curious), so it goes upstream at x-2 kilometers per hour. And the journey takes it 24 kilometers against that sneaky current of 2 kilometers per hour.
After enduring that exercise, the boat decides to have a little more fun and heads back downstream with the current of 2 kilometers per hour. This time, it can happily move at a faster pace of x+2 kilometers per hour.
So, my friend, the boat's adventure finally ends when it returns having traveled 24 kilometers upstream and then back downstream. Phew! That was quite the voyage. I hope my little humor helped make this current information a bit more entertaining. Let me know if there's anything else I can float your way!
To find the speed of the boat in still water, we can use the concept of relative velocity.
Let's say the speed of the boat in still water is represented by "B" km/h. Since the boat is moving upstream, against the current, its effective speed will be reduced by the speed of the current (2 km/h). Therefore, the speed of the boat upstream is B - 2 km/h.
Similarly, when the boat moves downstream, its effective speed will be increased by the speed of the current (2 km/h). So, the speed of the boat downstream is B + 2 km/h.
Now, we can calculate the time taken for each leg of the journey using the formula: Time = Distance / Speed.
For the upstream journey:
Time upstream = Distance upstream / Speed upstream
Time upstream = 24 km / (B - 2) km/h
For the downstream journey:
Time downstream = Distance downstream / Speed downstream
Time downstream = 24 km / (B + 2) km/h
Since the boat travels the same distance upstream and downstream, the total time of the journey is the sum of the time spent upstream and downstream.
Total time = Time upstream + Time downstream
Now, let's put the equations together and solve for B:
Total time = 24 / (B - 2) + 24 / (B + 2)
To simplify this equation, we can find a common denominator, which in this case is (B - 2)(B + 2).
Total time = (24(B + 2) + 24(B - 2)) / (B - 2)(B + 2)
Expanding and simplifying:
Total time = (24B + 48 + 24B - 48) / (B^2 - 4)
Total time = (48B) / (B^2 - 4)
Now, we know that the total time taken is inversely proportional to the speed in still water:
Total time is inversely proportional to B
So, we can set up the following equation:
Total time = k / B
where k is a constant.
Combining the two equations:
(48B) / (B^2 - 4) = k / B
Cross-multiplying:
48B^2 = k(B^2 - 4)
48B^2 = kB^2 - 4k
Rearranging:
(k - 48)B^2 = -4k
Dividing both sides by (k - 48):
B^2 = -4k / (k - 48)
To solve for B, we need to know the value of k. Unfortunately, the given information does not provide the value of k, so we cannot determine the exact speed of the boat in still water based on the given information.