In the movement on the river" present speed: the speed (V) speed current (Vпо tech.), speed against the current (V [PR]. tech.), flow rate (Vтеч.). It should be noted that private speed boats is the speed in still water. To find the speed of the flow, it is necessary for the flow rate to add your own. To find the speed against the current, it is necessary from own rate, subtract the rate of flow.
The first thing you need to learn and know "by heart" formula. Record and remember:

Vпо tech=VC+Vтеч.

V [PR]. tech.=VC-Vтеч.

V [PR]. tech=tech Vпо. - 2Vтеч.

Vпо tech.=V [PR]. tech+2Vтеч.

Vтеч.=(Vпо tech. - V [PR]. tech)/2

VC=(Vпо tech.+V [PR] tech.)/2 or VC=Vпо tech.+Vтеч.
For example, let us consider how to find their own speed and to solve problems of this type.

Example 1.The speed of the boat upstream 21.8 km/h and upstream 17.2 km/h to Find a private speed boat and speed of river flow.

Solution: According to the formula: VC=(Vпо tech.+V [PR] tech.)/2 and Vтеч.=(Vпо tech. - V [PR]. tech)/2, we find:

Vтеч = (21,8 - 17,2)/2=4,6\2=2,3 (km/h)

VC = V [PR] tech.+Vтеч=17,2+2,3=19,5 (km/h)

Answer: Vc=19,5 (km/h), Vтеч=2,3 (km/h).
Example 2. The steamer passed upstream 24 miles and back, spending the trip back to 20 minutes less than when moving against the current. Find his own speed in still water if the speed of the current is 3 km/h.

For X take a private speed boat. Set up a table where you put all the data.

Against tech. The flow

Distance 24 24

Speed X-3 X+3

time 24/ (X-3) 24/ (X+3)

Knowing that on the way back the boat spent 20 minutes less time than on the path, we compose and solve the equation.

20 min=1/3 hours.

24/ (X-3) – 24/ (X+3) = 1/3

24*3(X+3) – (24*3(X-3)) – ((X-3)(X+3))=0




X=21(km/h) – private speed boat.

Answer: 21 km/h.