A fisherman traveled in a boat from point N upstream. After having traveled 6 km, he stopped rowing and 2 hour 40 min after first leaving N, he was brought back to N by the current. Knowing that the speed of the boat in still water is 9 km/hour, find the speed of the river’s current.
t = d / r
[6 / (9 - c)] + [6 / (9 + c)] = 8/3 hr
6(9 + c) + 6(9 - c) = 8/3(81 - c^2)
108 = 216 - (8/3 c^2) ... 0 = 108 -(8/3 c^2)
use quadratic formula to find c
Thx!
But, so is c the speed
To solve this problem, we can use the formula:
Speed of boat in still water = (Speed of boat downstream + Speed of boat upstream) / 2
Let's denote the speed of the river's current as 'c' (in km/hour).
Given information:
Speed of boat in still water = 9 km/hour
Distance travelled upstream = 6 km
Time taken downstream = 2 hours 40 minutes = 2.67 hours
Now, let's break down the problem:
1. Calculate the speed of the boat downstream:
When the boat is going downstream, the speed of the boat in still water is added to the speed of the river's current. So, the speed of the boat downstream is (9 + c) km/hour.
2. Calculate the time taken downstream:
We are given that the boat took 2 hours 40 minutes (or 2.67 hours) to cover the same distance downstream. Let's denote the time taken downstream as 't_d'.
Distance downstream = Distance upstream = 6 km (since the boat returns to point N)
Using the formula: Distance = Speed × Time, we can write:
6 = (9 + c) × t_d
t_d = 6 / (9 + c)
3. Calculate the speed of the boat upstream:
When the boat is going upstream, the speed of the river's current is subtracted from the speed of the boat in still water. So, the speed of the boat upstream is (9 - c) km/hour.
4. Calculate the time taken upstream:
We are given that it took 2 hours 40 minutes (or 2.67 hours) to cover the same distance while going downstream, which is also the time it took to travel upstream. Let's denote the time taken upstream as 't_u'.
Using the formula: Distance = Speed × Time, we can write:
6 = (9 - c) × t_u
t_u = 6 / (9 - c)
Since the fisherman stops rowing and is brought back to point N by the current, we know that the time taken upstream is equal to the time taken downstream:
t_u = t_d
Equating the equations for t_u and t_d:
6 / (9 - c) = 6 / (9 + c)
To solve for 'c', we can cross-multiply and solve the resulting equation:
6 * (9 + c) = 6 * (9 - c)
54 + 6c = 54 - 6c
Simplifying the equation:
12c = 0
c = 0
Therefore, the speed of the river's current is 0 km/hour. This means that there is no current in the river, and the fisherman's boat is not affected by any external force.