The current in a stream moves at a speed of 8mph. A boat travels 13 mph up stream and 13 mph downstream with a total time of 3 hrs. What is the speed of the boat is still water?
since time = distance/speed,
13/(x-8)+13/(x+8)=3
To find the speed of the boat in still water, we can use the concept of relative velocity. Let's say the speed of the boat in still water is x mph.
When the boat is traveling upstream (against the current), its effective speed is reduced by the speed of the current. So, the speed of the boat when traveling upstream would be (x - 8) mph.
When the boat is traveling downstream (with the current), its effective speed is increased by the speed of the current. So, the speed of the boat when traveling downstream would be (x + 8) mph.
The distance traveled by the boat when going upstream is the same as the distance traveled when going downstream. Let's denote this distance as d.
Using the formula speed = distance / time, we can write two equations:
d / (x - 8) = 3 [Equation 1]
d / (x + 8) = 3 [Equation 2]
Now, we can solve this system of equations to find the value of x.
From Equation 1, we have d = 3(x - 8).
Substituting this in Equation 2, we get:
3(x - 8) / (x + 8) = 3
Cross-multiplying, we have:
3(x - 8) = 3(x + 8)
Expanding and simplifying:
3x - 24 = 3x + 24
By cancelling out the 3x terms, we find:
-24 = 24
This is not a valid equation, which means there is no solution. It is impossible for the distance traveled upstream to be equal to the distance traveled downstream given the current speed and boat speeds.
Therefore, we cannot determine the speed of the boat in still water using the given information.