A boat is traveling in a river with a current that has a speed of 1.5 km/h. In one hour, the boat can travel twice the distance downstream as it can travel upstream. What is the boat's speed in still water?
To solve this problem, let's represent the boat's speed in still water by "x" km/h.
When the boat is traveling downstream (along the current), its effective speed will be the sum of the boat's speed in still water and the speed of the current. Thus, the boat's speed downstream will be (x + 1.5) km/h.
When the boat is traveling upstream (against the current), its effective speed will be the difference between the boat's speed in still water and the speed of the current. Thus, the boat's speed upstream will be (x - 1.5) km/h.
Given that the boat can travel twice the distance downstream than it can upstream in one hour, we can set up the equation:
Distance downstream = 2 * (Distance upstream)
Since speed is equal to distance divided by time, and the time is the same for both downstream and upstream, we can set up the following equation:
(x + 1.5) = 2 * (x - 1.5)
Now, let's solve for x:
x + 1.5 = 2x - 3
1.5 + 3 = 2x - x
4.5 = x
Therefore, the boat's speed in still water is 4.5 km/h.
Let's assume the speed of the boat in still water is "S" km/h.
When the boat is traveling downstream, the current aids its movement, so its effective speed is increased by the speed of the current. Therefore, the boat's speed downstream is (S + 1.5) km/h.
When the boat is traveling upstream, the current opposes its movement, so its effective speed is decreased by the speed of the current. Therefore, the boat's speed upstream is (S - 1.5) km/h.
We are given that in one hour, the boat can travel twice the distance downstream as it can travel upstream.
Let's say the distance the boat can travel downstream in one hour is "D" km. So, the distance it can travel upstream in one hour is (D/2) km.
Now, we can use the formula for speed: speed = distance/time.
The boat's speed downstream is (S + 1.5) km/h. The time taken to travel the distance downstream is 1 hour. So, we have the equation:
(S + 1.5) = D/1.
The boat's speed upstream is (S - 1.5) km/h. The time taken to travel the distance upstream is 1 hour. So, we have the equation:
(S - 1.5) = D/2.
Simplifying the equations, we have:
S + 1.5 = D.
S - 1.5 = D/2.
Now, we can solve these equations simultaneously.
Multiply the second equation by 2 to eliminate fractions:
2S - 3 = D.
Now, substitute D = S + 1.5 from the first equation into the second equation:
2S - 3 = S + 1.5.
Simplify the equation:
2S - S = 1.5 + 3.
Simplify further:
S = 4.5.
Therefore, the boat's speed in still water is 4.5 km/h.