The speed of a boat in still water is 8km/h. It travels upstream for a distance of 1.5km and returns(downstream) to the starting point. If the whole trip takes 2/5 hours, find the speed of the stream flow.
Since time = distance/speed,
1.5/(8-s) + 1.5/(8+s) = 0.4
s = 2
7.1km/hr
To find the speed of the stream flow, we need to consider the concept of relative speed.
Let's assume the speed of the stream flow as 'x' km/h.
When the boat is traveling upstream, it has to overcome the speed of the stream flow. So, the effective speed of the boat will be the difference between the speed of the boat in still water and the speed of the stream flow.
Therefore, the effective speed of the boat upstream = Speed of the boat in still water - Speed of the stream flow = 8 - x km/h
Similarly, when the boat is traveling downstream, it gets an additional boost from the stream flow. So, the effective speed of the boat downstream will be the sum of the speed of the boat in still water and the speed of the stream flow.
Therefore, the effective speed of the boat downstream = Speed of the boat in still water + Speed of the stream flow = 8 + x km/h
Now, let's calculate the time taken by the boat to travel upstream and downstream.
Time taken to travel upstream = Distance / Effective speed of the boat upstream
= 1.5 km / (8 - x) km/h
Time taken to travel downstream = Distance / Effective speed of the boat downstream
= 1.5 km / (8 + x) km/h
According to the given conditions, the total time taken for the round trip is 2/5 hours. So, we can write the equation:
Time taken to travel upstream + Time taken to travel downstream = 2/5
Substituting the values, we get:
1.5 / (8 - x) + 1.5 / (8 + x) = 2/5
Now, let's solve this equation to find the value of 'x'.
Multiplying the equation by (8 - x)(8 + x) to eliminate the denominators, we get:
1.5(8 + x) + 1.5(8 - x) = (2/5)(8 - x)(8 + x)
Now, simplify the equation:
12 + 1.5x + 12 - 1.5x = (2/5)(64 - x^2)
24 = (2/5)(64 - x^2)
Multiply both sides by 5 to get rid of the fraction:
120 = 2(64 - x^2)
120 = 128 - 2x^2
Rearrange to get a quadratic equation:
2x^2 = 128 - 120
2x^2 = 8
x^2 = 4
x = ± √4
Since the speed of the stream flow cannot be negative, we take x = √4
Therefore, the speed of the stream flow is 2 km/h.