The speed of a boat in still water is 29mph. if the boat travels 140mph downstream in the same time that it takes to travel 92miles upstream, find the speed of the stream.
distance=velocity*time
distanceupstream=(29+Vs)time
distancedownstream=(29-Vs)time
set the distances to bd 140 downstream, and 92 up
140=(29+vs)time
92=(29-Vs)time
or 140/92 =(29+Vs)/(29-Vs)
92(29+Vs)=140(29-Vs) and you solve for Vs
To find the speed of the stream, we need to set up an equation based on the given information.
Let's assume the speed of the stream is "x" mph.
When the boat is traveling downstream (in the same direction as the stream), its effective speed is the sum of its own speed in still water and the speed of the stream. So, the boat's speed downstream is 29 mph + x mph = 29 + x mph.
Similarly, when the boat is traveling upstream (against the stream), its effective speed is the difference between its own speed in still water and the speed of the stream. So, the boat's speed upstream is 29 mph - x mph = 29 - x mph.
Now, we know that the boat travels 140 miles downstream in the same time it takes to travel 92 miles upstream. We can set up the following equation:
140 / (29 + x) = 92 / (29 - x)
To solve this equation and find the value of x (the speed of the stream), we can cross-multiply:
140 * (29 - x) = 92 * (29 + x)
Simplifying this equation:
4060 - 140x = 2668 + 92x
Rearranging the terms:
140x + 92x = 4060 - 2668
232x = 1392
Dividing both sides by 232:
x = 1392 / 232
Calculating this:
x ≈ 6
Therefore, the speed of the stream is approximately 6 mph.