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Giải bài 2.17 trang 46 SGK Toán 8 - Cùng khám phá

Một đội máy xúc trên công trường nhận nhiệm vụ xúc
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Đề bài

Một đội máy xúc trên công trường nhận nhiệm vụ xúc \(17\,400\,{m^3}\) đất. Giai đoạn đầu, đội làm việc với năng suất trung bình \(x\,{m^3}\)/ngày và đào được \(7\,500\,{m^3}.\) Giai đoạn sau, năng suất của đội tăng \(25\,{m^3}\)/ngày. a) Viết phân thức theo \(x\) biểu diễn thời gian để đội đó hoàn thành công việc. b) Tính thời gian để đội đó hoàn thành công việc khi năng suất trung bình là \(250\,{m^3}\)/ngày.

Phương pháp giải - Xem chi tiết

a) Ta viết phân thức biểu diễn thời gian của đội ở hai giai đoạn rồi tính tổng hai phân thức vừa tìm được. b) Thay \(x = 250\) vào phân thức vừa tìm được ở câu a.

Lời giải chi tiết

a) Phân thức biểu diễn thời gian đội đó hoàn thành công việc là:\(\frac{{7500}}{x} + \frac{{17400 - 7500}}{{x + 25}} = \frac{{7500}}{x} + \frac{{9900}}{{x + 25}}.\)b) Thay \(x = 250\) ta được:\(\frac{{7500}}{{250}} + \frac{{9900}}{{250 + 25}} = 66.\)Vậy thời gian để đội đó hoàn thành công việc khi năng suất trung bình là \(250\,{m^3}\)/ngày là 66 ngày.

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