有數學題想問

a = length of Section A
b = length of Section B

Set up 2 equations:

1) 3/5a - 1/5 b = 4
2) a + b = 8

For 2),

a = 8 - B --> 3)

Substitute 3) to 1)

3/5 a - 1/5b = 4
3/5 x (8-b) - 1/5b = 4
24/5 - 3/5b - 1/5b = 4
24/5 - 4/5b = 4
24/5 - 4 = 4/5b
4/5 = 4/5 b
b = 1--> 4)

Substitute 4) to 2)
2) a + b = 8
a + 1 = 8
a = 7--> 5)

Substitute 4) and 5) into 1) with checking

1) 3/5a - 1/5b = 4

3/5 x 7 - 1/5 x 1
= 21/5 - 1/5
= 20/5
= 4
= Right hand side

Conclusion:

Which section of the Nature Education Track is longer? Section A or Section B?
Section A is longer.
Section A = 7 km
Section B = 1 km

By how many kilometres?
7 km – 1 km = 6km

let section A distance be x
let section B distance be y

3x/5 - y1/5 = 4 ---------- 1
x + y = 8 ---------- 2

from 2: x = 8 - y

sub x = 8-y into 1:
3(8-y)/5 - y/5 = 4
(24-3y-y)/5 = 4
24-4y = 20
4y = 4
y = 1

sub y = 1 into 2
x + 1 = 8
x = 8 - 1
x = 7

because x > y, so section A > section B
therefore, section A is longer

hence, 7km-1km = 6km, section A is longer than section B for 6km

你用英文問，我就用英文答你啦~

Let a be the length of section A, b be the length of section B.
a+b=8 --- (1)　(by "A Nature Education Track is 8 km long.")
(3/5)a - (1/5)b = 4 --- (2)　(by"It is known that Martin has walked 4 km more than Boddy."

(2)*5 : 3a-b=20 --- (3)
(1)+(3) : (a+b)+(3a-b)=8+20
　　　　　　　　4a=28
　　　　　　　　 a=7

sub a=7 into (1), 7+b=8
　　　　　　　　 b=1

Therefore,Section A is longer.
And It's longer than section B by (7-1)=6 kilometres.

1: A Nature Education Track is 8 km long: A + B = 8
2: Moreover, 3A/5 - B/5 = 4

from 2) 3A - B = 20, B = 3A-20
subs B into 1) A + 3A - 20 = 8
4A = 28
A = 7

so Section B is of 1km
Section A is longer than Section B by 7-1 = 6km

2007-04-08 13:30:52 補充：
係好長...