Пусть v - скорость заполнения первой трубой. Тогда v+5 - второй. Из условия:
![{200\over v}={200\over v+5}+2\\\\100v+500=100v+v^2+5v\\v^2+5v-500=0\\D=25+2000=2025=45^2\\v_1={-5+45\over2}=20\\v_2={-5-45\over2}, v\ \textgreater \ 0\\](https://tex.z-dn.net/?f=%7B200%5Cover+v%7D%3D%7B200%5Cover+v%2B5%7D%2B2%5C%5C%5C%5C100v%2B500%3D100v%2Bv%5E2%2B5v%5C%5Cv%5E2%2B5v-500%3D0%5C%5CD%3D25%2B2000%3D2025%3D45%5E2%5C%5Cv_1%3D%7B-5%2B45%5Cover2%7D%3D20%5C%5Cv_2%3D%7B-5-45%5Cover2%7D%2C+v%5C+%5Ctextgreater+%5C+0%5C%5C)
Ответ: 20 литров в минуту
Решение во вложенном файле
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![( \frac{11}{30}+ \frac{17}{30}) : \frac{19}{45}=\frac{11+17}{30}](https://tex.z-dn.net/?f=%28+%5Cfrac%7B11%7D%7B30%7D%2B+%5Cfrac%7B17%7D%7B30%7D%29+%3A+%5Cfrac%7B19%7D%7B45%7D%3D%5Cfrac%7B11%2B17%7D%7B30%7D+)
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![\frac{45}{19} = \frac{28}{30}](https://tex.z-dn.net/?f=+%5Cfrac%7B45%7D%7B19%7D+%3D+%5Cfrac%7B28%7D%7B30%7D)
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![\frac{45}{19} =](https://tex.z-dn.net/?f=+%5Cfrac%7B45%7D%7B19%7D+%3D+)
(сокращаем 30 и 45 на 15)
![\frac{28*3}{2*19}=](https://tex.z-dn.net/?f=+%5Cfrac%7B28%2A3%7D%7B2%2A19%7D%3D+)
(далее сокращаем 28 и 2 на 2)
![\frac{14*3}{19}= \frac{42}{19}=2 \frac{4}{19}](https://tex.z-dn.net/?f=+%5Cfrac%7B14%2A3%7D%7B19%7D%3D+%5Cfrac%7B42%7D%7B19%7D%3D2+%5Cfrac%7B4%7D%7B19%7D++)
![\frac{(b^{4} )^3}{b^7} = \frac{ b^{4*3} }{b^7}= \frac{b^{12} }{b^7}= b^{12-7}=b^5](https://tex.z-dn.net/?f=+%5Cfrac%7B%28b%5E%7B4%7D+%29%5E3%7D%7Bb%5E7%7D+%3D+%5Cfrac%7B+b%5E%7B4%2A3%7D+%7D%7Bb%5E7%7D%3D+%5Cfrac%7Bb%5E%7B12%7D+%7D%7Bb%5E7%7D%3D+b%5E%7B12-7%7D%3Db%5E5)
(Можно и короче записать)
![3 - \frac{x}{7}= \frac{x}{3} /*21](https://tex.z-dn.net/?f=+3+-+%5Cfrac%7Bx%7D%7B7%7D%3D+%5Cfrac%7Bx%7D%7B3%7D+%2F%2A21+)
(Приводим к общему знаменателю)
![3*21- \frac{x}{7}*21 = \frac{x}{3} *21 \\ 63-3x=7x](https://tex.z-dn.net/?f=3%2A21-+%5Cfrac%7Bx%7D%7B7%7D%2A21+%3D+%5Cfrac%7Bx%7D%7B3%7D+%2A21+%5C%5C+63-3x%3D7x)
Неизвестные перенесем в одну сторону, известные в другую с учетом правила - при переходе через знак "=", знак числа меняется на противоположный.
7х+3х=63
10х=63
![x= \frac{63}{10} \\ x=6,3](https://tex.z-dn.net/?f=x%3D+%5Cfrac%7B63%7D%7B10%7D++%5C%5C+x%3D6%2C3)
![\left \{ {{3x+2y=8} \atop {4x-y=7}} \right. \left \{ {{3x+2(4x-7)=8} \atop {y=4x-7}} \right. \left \{ {{3x+8x-14=8} \atop {y=4x-7}} \right. \left \{ {{11x-14=8} \atop {y=4x-7}} \right. \\ \\ \left \{ {{11x=8+14} \atop {y=4x-7}} \right. \left \{ {{11x=22} \atop {y=4x-7}} \right. \left \{ {{x= \frac{22}{11} } \atop {y=4x-7}} \right. \left \{ {{x=2} \atop {y=4*2-7}} \right. \left \{ {{x=2} \atop {y=1}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B3x%2B2y%3D8%7D+%5Catop+%7B4x-y%3D7%7D%7D+%5Cright.++++%5Cleft+%5C%7B+%7B%7B3x%2B2%284x-7%29%3D8%7D+%5Catop+%7By%3D4x-7%7D%7D+%5Cright.++%5Cleft+%5C%7B+%7B%7B3x%2B8x-14%3D8%7D+%5Catop+%7By%3D4x-7%7D%7D+%5Cright.+++%5Cleft+%5C%7B+%7B%7B11x-14%3D8%7D+%5Catop+%7By%3D4x-7%7D%7D+%5Cright.++%5C%5C+%5C%5C+%5Cleft+%5C%7B+%7B%7B11x%3D8%2B14%7D+%5Catop+%7By%3D4x-7%7D%7D+%5Cright.++%5Cleft+%5C%7B+%7B%7B11x%3D22%7D+%5Catop+%7By%3D4x-7%7D%7D+%5Cright.+%5Cleft+%5C%7B+%7B%7Bx%3D+%5Cfrac%7B22%7D%7B11%7D+%7D+%5Catop+%7By%3D4x-7%7D%7D+%5Cright.+++%5Cleft+%5C%7B+%7B%7Bx%3D2%7D+%5Catop+%7By%3D4%2A2-7%7D%7D+%5Cright.+++%5Cleft+%5C%7B+%7B%7Bx%3D2%7D+%5Catop+%7By%3D1%7D%7D+%5Cright.++)
(2a+1)(a-3)+3-2a²=2a²-6a+a-3+3-2a²=-5a
-5*1=-5