Let the speed of the boat be B km/hr and let the time taken to travel 4 km downstream be t hours.
Since the boat is travelling with the current downstream, the effective speed is (B + 3) km/hr. Therefore, the time taken to travel 4 km downstream is:
t = 4 / (B + 3)
It is given that the boat takes twice as long to travel 3 km upstream, which means the time taken to travel 3 km upstream is 2t.
Since the boat is now travelling against the current upstream, the effective speed is (B - 3) km/hr. Therefore, the time taken to travel 3 km upstream is:
2t = 3 / (B - 3)
We now have two equations in two variables (t and B). To solve for B, we can rearrange the second equation to get:
B = 3 / (2t) + 3
Substituting this expression for B into the first equation, we get:
t = 4 / (3 / (2t) + 6)
Simplifying this expression, we get:
t = 8t / (9 + 4t)
Multiplying both sides by (9 + 4t), we get:
t(4t + 9) = 8t
Expanding and rearranging, we get:
4t^2 - 8t + 9t =0
4t^2 + t - 0 = 0
Using the quadratic formula, we get:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 4, b = 1, and c = 0.
Substituting these values, we get:
t = (-1 ± sqrt(1^2 - 4(4)(0))) / 2(4)
Simplifying, we get:
t = (-1 ± sqrt(1)) / 8
t = -0.125 or t = 0.25
Since time cannot be negative, we take t = 0.25 hours.
Substituting this value of t into the equation for B that we derived earlier, we get:
B = 3 / (2t) + 3 = 3 / (2 * 0.25) + 3 = 15 km/hr
Therefore, the speed of the boat is 15 km/hr, and the time taken to travel 10 km upstream (against the current) is:
t = 10 / (15 - 3) = 0.77 hours (rounded to two decimal places)
So it will take the man approximately 0.77 hours, or 46 minutes and 12 seconds, to get to his fishing spot upstream.