A girl rows 10 km downstream in 2 h. Her return trip takes 3 h. How fast is the current. in km/
v = her speed
c = current speed
(v+c) * 2 = 10
(v-c) * 3 = 10
v + c = 5 = 15/3
v - c = 10/3
--------------subtract
2 c = 5/3
c = 5/6
To find the speed of the current, we need to use the formula:
Speed = Distance / Time
Let's assume the speed of the girl in still water (when there is no current) is V km/h, and the speed of the current is C km/h.
For the downstream trip:
The girl rows with the current, so her effective speed is increased by the speed of the current. Therefore, her speed is (V + C) km/h.
Using the formula, we have:
(V + C) = 10 km / 2 h
Simplifying the equation:
V + C = 5 km/h
For the return trip:
The girl rows against the current, so her effective speed is decreased by the speed of the current. Therefore, her speed is (V - C) km/h.
Using the formula again, we have:
(V - C) = 10 km / 3 h
Simplifying the equation:
V - C = 10/3 km/h
Now, we have two equations:
V + C = 5 km/h
V - C = 10/3 km/h
We can solve these equations simultaneously to find the values of V and C. Adding the two equations together, the C terms cancel out:
(V + C) + (V - C) = 5 km/h + 10/3 km/h
2V = 15/3 km/h
V = 7.5/3 km/h
V = 2.5 km/h
Now we can substitute the value of V into one of the original equations to find C:
2.5 km/h + C = 5 km/h
C = 5 km/h - 2.5 km/h
C = 2.5 km/h
Therefore, the speed of the current is 2.5 km/h.