The solution of tasks on "the movement on water" troubles much. In them there are several types of speeds therefore decisive I begin to be confused. To learn to solve problems of this kind, it is necessary to know definitions and formulas. The ability to make schemes very much facilitates understanding of a task, promotes the correct drawing up the equation. And correctly worked out equation - the most important in the solution of any type of tasks.
Instruction
1. At tasks "on the movement down the river" there are speeds: own speed (Vc), speed on a current (Vpo to flow.), speed against the current (Vpr. leak.), current speed (Vtech.). It should be noted that own speed of water court is a speed in still water. To find speed on a current, it is necessary to add own to the speed of a current. To find speed against the current, it is necessary to subtract current speed from own speed.
2. The first that it is necessary to teach also the nobility ""on teeth"" - formulas. Write down and remember: Vpo =Vc leak +vtech.Vpr. leak.=vs-Vtech.Vpr. leak =vpo leak. - 2vtech.Vpo leak.=vpr. leak +2vtech.Vtech. = (Vpo to flow. - Vpr. leak) / 2Vc = (Vpo leak.+vpr leak.)/2 or Vc =vpo leak.+vtech.
3. On an example we will sort how to find own speed and to solve problems of this kind. Example 1. Boat speed on a current 21.8km/h, and against the current 17.2 km/h. To find own speed of the boat and speed of a watercourse. Decision: According to formulas: Vc = (Vpo leak.+vpr leak.)/2 and Vtech. = (Vpo to flow. - Vpr. a leak)/2, we will find: Vtech = (21.8 - 17.2)/2=4.6\2=2.3 (km/h) of Vc = Vpr leak.+vtech of =17.2+2.3=19.5 (km/h) Answer: Vc=19.5 (km/h), Vtech of =2.3 (km/h).
4. Example 2. The steamship passed against the current 24 km and returned back, having spent for a way back 20 min. smaller, than at the movement against the current. Find its own speed in motionless water if the speed of a current is equal to 3 km/h. We will take own speed of the steamship for X. Let's make the table where we will enter all data. Against a leak. On a techeniyurasstoyaniye +3vremya 24/(H-3) 24/(X +3) Knowing 24 24 Speed of H-3 H that the steamship spent for a way back for 20 minutes of time less, than on the way on a current, we will make and we will solve the equation.20 min. =1/3 hour.24/(H-3) – 24/(X +3) = 1/324*3 (X +3) – (24*3(H-3)) – ((H-3) (X +3)) = 072X+216-72X+216-X2+9=0441-X2=0X2=441X=21 (km/h) – own speed of the steamship. Answer: 21 km/h.