Предмет: Математика, автор: mmmmjy

катер прошёл расстояние между пристанями туда и обратно за 4,5 ч.Скорость течения реки 2 км.ч.Собственная скорость катера 18 км.ч.Найдите расстояние между пристанями.

Ответы

Автор ответа: 5roGest
0

Скорость катера против течения будет равна 18 - 2 = 16 км/ч                \V_1

Скорость катера по течению будет равна 18 + 2 = 20 км/ч                       \V_2

Время затраченное туда и обратно 4,5 ч                                                       \t

Растояния не менялись поэтому растояние туда равно растоянию обратно.

                                                                                                                                   \S_1=S_2

 

V=frac{S}{t}

 

t=frac{S}{V}

 

 

t_1=frac{S_1}{V_1}

 

t_2=frac{S_2}{V_2}

 

t_1+t_2=t

 

 

 

frac{S}{V_1}+frac{S}{V_2}=4,5

 

frac{Stimes V_2+Stimes V_1}{V_1times V_2}=4,5

 

frac{S( V_2+V_1)}{V_1 V_2}=4,5

 

S( V_2+V_1)=4,5V_1 V_2

 

S=frac{4,5V_1 V_2}{V_2+V_1}

 

S=frac{4,5times 16times20}{20+16}

 

S=frac{1440}{36}

 

 

S=40 км

 

 

Ответ: 40 км расстояние между пристанями.

 

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