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angel 發問於 科學及數學數學 · 1 十年前

Simultaneous Linear Equations in Two Unknowns (f.2)

我想要steps 同解釋.....唔該.....

1). Tim and David are 20km apart . If they walk towards each other,they will meet in 2 hours.If theywalk towards the same direction and Tim is behind David,Tim will catch up with David in 5 hours .Find their speed. (Let x km/h be the speed of Tim, y km/h of David.)

2).A sum of money is divided betweenAmy and Bob in the ratio 7:4 . If Amy gives $600 to Bob , the new ratio is 5:6.

a). How much do Amy and Bob get originally.

b). What is the sum of money.

2 個解答

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  • sunny
    Lv 5
    1 十年前
    最愛解答

    1). Tim and David are 20km apart . If they walk towards each other,they will meet in 2 hours.If theywalk towards the same direction and Tim is behind David,Tim will catch up with David in 5 hours .Find their speed. (Let x km/h be the speed of Tim, y km/h of David.)

    Let x km/h be the speed of Tim, y km/h of David.

    2x + 2y = 20....................(1)

    5x = 5y + 20....................(2)

    From (1),

    x + y = 10........................(3)

    From (2)

    x = y + 4...........................(4)

    Sub. (4) into (3)

    y + 4 + y = 10

    2y = 6

    y = 3 //

    Sub. y = 3 into (3)

    x + 3 = 10

    x = 7 //

    The speed of Tim is 7km/h , the speed of David is 3km/h

    2).A sum of money is divided betweenAmy and Bob in the ratio 7:4 . If Amy gives $600 to Bob , the new ratio is 5:6.

    a). How much do Amy and Bob get originally.

    A sum of money is divided betweenAmy and Bob in the ratio 7:4 . If Amy gives $600 to Bob , the new ratio is 5:6.

    Let Amy get $ a and Bob get $b originally

    a/b = 7/4............(1)

    (a - 600) / (b+600) = 5/6.......(2)

    From (1), we know that,

    4a = 7b

    a = 7b / 4........................(3)

    From (2), we know that,

    5(b+600) = 6(a - 600)

    5b + 3000 = 6a - 3600

    5b + 6600 = 6a

    6a - 5b = 6600................(4)

    Substitute (3) into (4)

    6( 7b/4 ) - 5b = 6600

    ( 42b/4 ) - 5b = 6600

    42b - 20b = 26400

    22b = 26400

    b = 1200 //

    Substitute b = 1200 into (3)

    a = 7(1200) / 4

    a = 8400 / 4

    a = 2100 //

    Amy get $ 2100, Bob get $ 1200

    b). What is the sum of money.

    2100 + 1200

    = 3300 //

    The sum of money is $3300

    2007-02-10 15:35:12 補充:

    Hints for question 2a : b = a / b , c : d = c / d , if a / b = c / d then ad = bc

    2007-02-11 11:59:08 補充:

    正確解釋應該如下: 1. Tim 和 David 相隔 20 公里,若他們同時相向而行,則會於2小時後相遇;若他們同時同向而行,而 Tim 跟在 David 後面,則 Tim 會於5小時後趕上 David。求他們二人的速率。( 設 Tim 的速率為 x km/h,David 的速率為 y km/h )2. 一筆錢以 7 : 4 之比例分別分給 Amy 和 Bob,若 Amy 給 Bob $600, 他們的比例會變成 5 : 6 。a ) 求 Amy 和 Bob 原有多少錢。b ) 求 這筆錢的金額

    資料來源: me~
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  • 1 十年前

    1.)Tim 和大衛是20km 單獨。如果他們走往彼此, 他們將見面在2 個小時。如果他們走往同樣方向並且Tim 是在大衛之後, Tim 將跟上大衛在5 個小時。發現他們的速度。(讓x km/h 是Tim 的速度, y km/h 大衛。)

    2)一個款項被劃分在艾米和鮑伯之間在比率7:4 。如果艾米給$600 鮑伯, 新比率是5:6 。

    a)多少做艾米和鮑伯最初得到。

    b)什麼是款項

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