(2006,河北)甲、乙兩個(gè)工程隊(duì)分別同時(shí)開(kāi)挖兩段河渠,所挖河渠的長(zhǎng)度y(m)與挖掘時(shí)間x(h)之間的關(guān)系如圖所示,請(qǐng)根據(jù)圖象所提供的信息解答下列問(wèn)題:

(1)乙隊(duì)開(kāi)挖到30m時(shí),用了________h.開(kāi)挖6h時(shí),甲隊(duì)比乙隊(duì)多挖了________m;

(2)請(qǐng)你求出:

①甲隊(duì)在0≤x≤6的時(shí)段內(nèi),yx之間的函數(shù)關(guān)系式;

②乙隊(duì)在2≤x≤6的時(shí)段內(nèi),yx之間的函數(shù)關(guān)系式.

(3)當(dāng)x為何值時(shí),甲、乙兩隊(duì)在施工過(guò)程中所挖河渠的長(zhǎng)度相等?

答案:2,10;y=10x,y=5x+20;x=4
解析:

解:(1)2 10

(2)①設(shè)甲隊(duì)在0x6的時(shí)段內(nèi)yx之間的函數(shù)關(guān)系式為

由圖可知,函數(shù)圖象過(guò)點(diǎn)(6,60)

,解得y=10x

設(shè)乙隊(duì)在2x6的時(shí)段內(nèi)yx之間的函數(shù)關(guān)系式為

由圖可知,函數(shù)圖象過(guò)點(diǎn)(2,30)(6,50)

解得y=5x20;

(3)由題意,得10x=5x20,解得x=4

當(dāng)x4h時(shí),甲、乙兩隊(duì)所挖的河渠長(zhǎng)度相等,


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