The speed of a stream is 3 km/h. A boat travels 25 km upstream in the same time it takes to travel 35 km downstream. What is the speed of the boat in still water?
speed of boat in still water ---> x km/h
time to go 25km upstream = 25/(x-3)
time to go 35 km downstream = 35/(x+3)
but those two times are supposed to be equal, so ..
25/(x-3) = 35/(x+3)
cross-multiply, then solve for x
To find the speed of the boat in still water, we need to set up an equation based on the given information.
Let's assume the speed of the boat in still water is 'x' km/h.
The boat travels 25 km upstream in the same time it takes to travel 35 km downstream. When the boat is moving upstream, it is going against the stream, so its effective speed is reduced.
The effective speed of the boat when moving upstream is (x - 3) km/h because the stream is working against the boat's motion and slowing it down by 3 km/h.
Similarly, when the boat is moving downstream, it is going with the stream, so its effective speed is increased.
The effective speed of the boat when moving downstream is (x + 3) km/h because the stream is aiding the boat's motion and increasing its speed by 3 km/h.
Now, we know that the time taken to travel a certain distance is given by the formula:
Time = Distance / Speed
Let's calculate the time for both cases:
Time taken when traveling upstream = 25 km / (x - 3) km/h
Time taken when traveling downstream = 35 km / (x + 3) km/h
According to the given information, both these times are the same. Therefore, we can set up the equation:
25 / (x - 3) = 35 / (x + 3)
To solve this equation, we can cross multiply:
25(x + 3) = 35(x - 3)
25x + 75 = 35x - 105
Now, let's simplify:
10x = 180
Dividing both sides by 10:
x = 18
Hence, the speed of the boat in still water is 18 km/h.