Предмет: Алгебра, автор: gagarinsashuta

из села вишнёвое в село яблоневое ,расстояние между которыми равно 15 км,всадник проскакал с некоторой скоростью .Возвращался он со скоростью на 3 км/ч большей и потратил на обратный путь на 15 мин меньше ,чем на путь из вишнёвого в яблоневое .Найдите первоначальную скорость

Ответы

Автор ответа: DariosI

0

15 мин=15/60 ч=0,25 ч

Пусть скорость всадника х км/ч, тогда на пути обратно скорость всадника (х+3) км/ч. Значит время потраченное из Вишневого в Яблоневый 15/х ч, а время обратно 15/(х+3) ч. Составим и решим уравнение:

15/х-15/(х+3)=0,25

15*4(х+3-х)=х²+3х

х²+3х=180

х²+3х-180=0

D=3²+4*180=729=27²

x₁=(-3+27)/2=12 км/ч скорость всадника

х₂=(-3-27)/2=-15<0 не подходит

Ответ первоначальная скорость всадника 12 км/ч

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