Solution of A curious trip on the river
WITHOUT EQUATIONS
The boat from the moment it crosses the bridge moves 20 minutes upstream. After that at the same speed it goes downhill. The duration of the return will be the same time, equal to 20 minutes The boat returns to the life preserver then after 40 minutes.
In the meantime, compared to the banks of the river, the life preserver fell by 1 km.
The speed of the life preserver (and the current of the river) is therefore 1:40/60=x:60. The speed is 1.5 km/hV
WITH EQUATIONS
Solution of the boat-life-bridge question in the PONTE (or RIVA) reference system
So we put ourselves in the shoes of an observer stationary on deck P, or stationary on shore (no matter in what position)
So in the text of the problem it says that:
Vα is the speed of the boat relative to the shore when traveling upstream •
Vβ is the speed of the boat relative to water •
Vαβ is the speed of the water relative to the bridge (and to the shore), the unknown of the problem with these symbols we mean positive quantities; if we consider positive the speed upstream, we will have that:• while the boat goes upstream its speed is Vα = Vβ Vαβ
- when going downstream, to retrieve the bottle, its speed is Vα = Vβ VαβTo determine Vαβ consider that in the time that the bottle takes to travel 1 km
carried by water, then at speed Vαβ, the boat proceeds for 20 min at speed Vα to the point R (inversion) and from point R to point B (where it retrieves the bottle) at speed
Vα = Vβ Vαβ. Let us equal these two times:
1km =20min+(Vβ Vαβ) 20min+1km
Vαβ (Vβ + Vαβ)
We develop the calculations for solution of A curious trip on the river :
1km⋅(Vβ +Vαβ)=20min⋅(Vβ +Vαβ)⋅Vαβ +(Vβ −Vαβ)⋅20min⋅Vαβ +1km⋅Vαβ 1km⋅(Vβ +Vαβ)=20min⋅(Vβ +Vαβ)⋅Vαβ +(Vβ −Vαβ)⋅20min⋅Vαβ +1km⋅Vαβ
1km Vβ =40min Vβ Vαβ
From which we get that the water speed relative to the bridge and the shore is
Vαβ= 1km =1,5km 40min h
So the boat from the moment it crosses the bridge moves 20 minutes upstream. After that at the same speed it goes downhill. The duration of the return will be the same time, equal to 20 minutes The boat returns to the life preserver then after 40 minutes.
In the meantime, compared to the banks of the river, the life preserver fell by 1 km.
At the end the speed of the life preserver (and the current of the river) is therefore 1:40/60=x:60. Speed is 1.5 km/h
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