The speed of a river current is 4 mph. IF a boat travels 20 miles downstream in the same time that it takes to travel 10 miles upstream, find the speed of the boat in still water.
downstream speed = u + 4
upstream speed = u - 4
20 = (u+4) t
10 = (u-4)t
so
20/(u+4) = 10/(u-4)
10 u + 40 = 20 u - 80
10 u = 120
u = 12 miles/hr
Why did the boat go downstream?
Because it didn't want to row!
But in all seriousness, let's solve this problem. Let's call the speed of the boat in still water "x" mph.
When the boat travels downstream, it gets a boost from the current. So the effective speed is x + 4 mph.
When the boat travels upstream, it has to fight against the current. So the effective speed is x - 4 mph.
We know that the boat travels 20 miles downstream in the same time it takes to travel 10 miles upstream.
So we can set up an equation:
20 / (x + 4) = 10 / (x - 4)
Now let's cross multiply and solve for x:
20(x - 4) = 10(x + 4)
20x - 80 = 10x + 40
10x = 120
x = 12
So the speed of the boat in still water is 12 mph.
To find the speed of the boat in still water, let's assume it is denoted by B mph.
When the boat travels downstream, it moves in the same direction as the river current. Therefore, the effective speed of the boat is the sum of its speed in still water and the speed of the river current, which is B + 4 mph.
On the other hand, when the boat travels upstream, it moves against the direction of the river current. Hence, the effective speed of the boat is the difference between its speed in still water and the speed of the river current, which is B - 4 mph.
Now, we are given that the boat travels 20 miles downstream in the same time that it takes to travel 10 miles upstream.
We can use the formula:
Time = Distance / Speed
Let's set up two equations based on the given information.
For downstream travel:
Time taken = Distance / Speed
Time taken = 20 miles / (B + 4 mph)
For upstream travel:
Time taken = Distance / Speed
Time taken = 10 miles / (B - 4 mph)
Since the time taken is the same for both cases, we can equate the two equations:
20 / (B + 4) = 10 / (B - 4)
Now, we can solve this equation to find the value of B, the speed of the boat in still water.
Cross-multiplying the equation gives:
20(B - 4) = 10(B + 4)
20B - 80 = 10B + 40
20B - 10B = 40 + 80
10B = 120
B = 120 / 10
B = 12
Therefore, the speed of the boat in still water is 12 mph.
To find the speed of the boat in still water, we need to set up an equation based on the given information.
Let's denote the speed of the boat in still water as "x" (in mph).
When the boat travels downstream (i.e., in the same direction as the current), the effective speed of the boat is the sum of the speed of the boat in still water and the speed of the current. So, the effective speed downstream is (x + 4) mph.
In the same amount of time, when the boat travels upstream (i.e., against the current), the effective speed of the boat is the difference between the speed of the boat in still water and the speed of the current. So, the effective speed upstream is (x - 4) mph.
According to the problem, the boat travels 20 miles downstream in the same time that it takes to travel 10 miles upstream.
Using the formula distance = speed × time, we can set up the following equation:
20 / (x + 4) = 10 / (x - 4)
To solve this equation, we can cross-multiply:
20(x - 4) = 10(x + 4)
20x - 80 = 10x + 40
20x - 10x = 40 + 80
10x = 120
x = 120 / 10
x = 12 mph
Therefore, the speed of the boat in still water is 12 mph.