一条公路上,一次有A、B、C三站,甲车从A站出发途经B站驶往目的地C站,乙车从C站出发驶往A站,甲乙两车行驶的时间为x(

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  • (1)由已知图象得:甲的速度为100km/h,乙的速度为50km/h,

    答:甲、乙两车的速度分别为100km/h,50km/h.

    (2)设乙车从B地返回到C地的函数解析式是y=kx+b

    ∵图象经过(5,0),(9,200)两点).

    ∴5k+b=09k+b=200

    解得:$left{begin{array}{l}{k=50}\{b=-250}end{array}right.$,

    ∴y=50x-250,

    答:乙车从B地返回到C地的过程中,y与x之间的函数关系式为y=50x-250.

    (3)设甲车从A地到B地的函数解析式是y1=k1x+b1,

    ∵图象经过(0,600),(6,0)两点,

    ∴$left{begin{array}{l}{600={b}_{1}}\{0=6{k}_{1}+{b}_{1}}end{array}right.$,解得:$left{begin{array}{l}{{k}_{1}=-100}\{{b}_{1}=;600}end{array}right.$,∴y1=-100x+600,

    设甲车从B地到C地的函数解析式是y2=k2x+b2,

    ∵图象经过(8,200),(6,0)两点,

    ∴$left{begin{array}{l}{0=6{k}_{2}+{b}_{2}}\{200=8{k}_{2}+{b}_{2}}end{array}right.$,解得:$left{begin{array}{l}{{k}_{2}=100}\{{b}_{2}=-;600}end{array}right.$,∴y2=100x-600,

    由$left{begin{array}{l}{y=50x-250}\{{y}_{1}=-100x+600}end{array}right.$和$left{begin{array}{l}{y=50x-250}\{{y}_{2}=100x-600}end{array}right.$,

    解得:y=$frac{100}{3}$(千米)和y=100(千米).

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