Simultaneous Linear Equations in Two Unknowns (f.2)

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

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