It takes a boat going upstream 3 hours to cover the same distance, as it would cover in 2 hours going downstream. What is the speed of the boat if the speed of the current is 3 kilometers per hour?
d = (Vb-Vc)*T1 = (Vb+Vc)*T2
(Vb-3)*3 = (Vb+3)*2
3Vb-9 = 2Vb+6
Vb = 15 km/h.
3 (b - 3) = 2 (b + 3)
3 b - 9 = 2 b + 6
15 km
15 km/h
Yes, the speed of the boat is 15 km/h.
Well, well, well! Looks like we've got ourselves a boat puzzle here. Let's unravel it, shall we?
Let's call the speed of the boat "B" and the speed of the current "C". Going upstream, the boat's effective speed is reduced, while going downstream, it gets a boost.
Now, given that it takes the boat 3 hours to cover a certain distance against the current, and 2 hours to cover the same distance with the current, we can set up two lovely equations for our amusement:
Distance = (B - C) * 3 (going upstream)
Distance = (B + C) * 2 (going downstream)
But since we're talking about the same distance, we can equate these two expressions and let the humor unfold:
(B - C) * 3 = (B + C) * 2
Expanding this equation, you get:
3B - 3C = 2B + 2C
Now, let's gather our B's and C's together and make them all feel cozy:
3B - 2B = 2C + 3C
Simplifying the equation:
B = 5C
Eureka! We've just uncovered the relationship between the boat's speed and the speed of the current. The boat's speed is five times the speed of the current!
Therefore, if the speed of the current is 3 kilometers per hour, the speed of the boat would be 5 times that, which is 15 kilometers per hour.
Hope that helps, dear sailor! Just remember to bring your sense of humor on board. Bon voyage! 🚤😄
To find the speed of the boat, we need to use the concept of relative speed.
Let's assume the speed of the boat (in still water) is denoted as B, and the speed of the current is denoted as C. The boat's speed will be affected by the current when it is moving upstream or downstream.
When the boat is moving upstream, it goes against the current, so its effective speed will be reduced. The boat's speed relative to the water will be B - C.
When the boat is moving downstream, it goes with the current, so its effective speed will increase. The boat's speed relative to the water will be B + C.
According to the question, the boat takes 3 hours to cover a certain distance when going upstream, and it takes 2 hours to cover the same distance when going downstream.
Let's denote the distance as D.
When going upstream, the boat's speed relative to the water is B - C, so the equation becomes:
D = (B - C) * 3
When going downstream, the boat's speed relative to the water is B + C, so the equation becomes:
D = (B + C) * 2
We now have a system of linear equations:
1) D = (B - C) * 3
2) D = (B + C) * 2
To solve this system of equations, we can set them equal to each other:
(B - C) * 3 = (B + C) * 2
Now, let's simplify and solve for B (the speed of the boat):
3B - 3C = 2B + 2C
Simplifying further:
3B - 2B = 2C + 3C
B = 5C
So, the speed of the boat (in still water) is 5 times the speed of the current.
Since the speed of the current is given as 3 kilometers per hour, the speed of the boat is:
B = 5C = 5 * 3 = 15 kilometers per hour.