a boat goes 16 Km upstream and 24 Km downstream in 6hrs.it can go 12Km upstream and 36 Km in same time.find the speed of boat in still water and speed of the stream
look at the algebraic equation that u posted previously. try to form an equation similar to that.
There is something inconsistent with the way this problem is stated. The ratio of upstream to downstream travel time should be independent of how far one travels. The second sentence is unecessary and inconsistent.
Let V be the speed in still water and v be the stream velocity
16/(V-v) = 6
24/(V+v) = 6
16 = 6V - 6v
24 = 6V + 6v
40 = 12V
V = 3.33 km/h
6v = 24 - 20 = 4 km/h
v = 0.67 km/h
To find the speed of the boat in still water, let's denote it as 'b', and the speed of the stream as 's'.
Let's start by considering the first scenario, where the boat goes 16 km upstream and 24 km downstream in 6 hours.
When the boat is traveling upstream, its effective speed is decreased by the speed of the stream, so it becomes (b - s).
When the boat is traveling downstream, its effective speed is increased by the speed of the stream, so it becomes (b + s).
Using the formula Time = Distance / Speed, we can write two equations for this scenario:
16 / (b - s) = t₁ --- (1)
24 / (b + s) = t₂ --- (2)
Now, let's consider the second scenario, where the boat goes 12 km upstream and 36 km downstream in the same amount of time. We'll call this time 't'.
Using the same equations as before, we can write:
12 / (b - s) = t --- (3)
36 / (b + s) = t --- (4)
Now, we have 4 equations in 4 unknowns (b, s, t₁, t). However, we only need to find the values of 'b' and 's'.
Solving these equations simultaneously will give us the values of 'b' and 's'. To do this, we can make use of the method of substitution or elimination.
Subtracting equations (1) and (2), we can eliminate 't₂' and solve for 't₁':
(16 / (b - s)) - (24 / (b + s)) = 0
Simplifying this equation gives us:
(16b + 16s - 24b + 24s) / (b² - s²) = 0
Simplifying further:
8s = 8b
Dividing both sides by 8:
s = b
So, we have found that the speed of the stream is equal to the speed of the boat in still water.
Substituting this result into equations (3) and (4), we get:
12 / (b - b) = t
36 / (b + b) = t
Simplifying further:
12 / 0 = t
36 / (2b) = t
Since time cannot be zero, we can conclude that equation (3) is not possible.
Therefore, we need to use equation (4) to find the value of 'b':
36 / (2b) = t
To simplify this equation, we need to know the value of 't'. Unfortunately, the given information does not provide the value of 't'.
Therefore, it is not possible to determine the exact values of the speed of the boat in still water ('b') or the speed of the stream ('s') without the value of 't'.