代數maths

1.In a hike, Jacky's speend walking uphill was 2km/h,and his speed walking downhill was 3km/h.The distance downhill is 1km longer than the distance uphill.He spent 3 hours and 40 minutes to finish the whole journey. Find the distance of whole journey.
設上山的距離為 x，下山的距離為x+1，則
(x / 2) + (x + 1)/3 = 3 + 40/60 = 22/6
全式乘6
3x +2(x+1) = 22
3x + 2x + 2 = 22
5x = 20
x = 4(km)
所以下山的距離為 x+1 = 5(km)
全程距離為 4 + 5 = 9(km)

2.If the solution of two equation2(x-1)=a-xan d3(x-2)=a-x are the same,find the value of a.
2(x-1) = a - x
及
3(x-2) = a-x
的解相同
則
2(x-1) = a-x = 3(x-2)
2x – 2 = 3x – 6
4 = x
將 x = 4 代入
2(x-1) = a – x
得
2(4-1) = a – 4
6 = a – 4
a = 10
所以 a 為 6

2. 2(x-1)=3(x-2)=a-x
2(x-1)=3(x-2)
2x-2 =3x-6
2x-2+6=3x
2x+4=3x
4=3x-2x
4=x
x=4

3(4-2)=a-4
6=a-4
a=10

1.Let the distance of whole journey is x. (the distance uphill is y)
y/2+(y+1)/3=3(2/3) <3.66666666> hour (the distance downhill is y+1)
(3y+2y+2)/6=3(2/3)
(5y+2)/6=3(2/3)
5y+2=22
5y=20
y=4

the distance uphill=4km
the distance downhill =5km
the distance of whole journey=9km

1.

Let x be the uphill distance.
Then (x+1) is the downhill distance.

Time of Jacky's uphill = x/2
Time of Jacky's downhill = (x+1)/3

(x/2) + (x+1)/3 = 3+(40/60)
3x+2(x+1) 2
-------------- = 3+ --
6 3

3x+2x+2 11
-------------- = ----
6 3
5x+2 22
-------- = ---
6 6
5x+2=22
5x=22-2
5x=20
x=20/5
x=4

Ans: The distance of whole journey is (4+4+1)=9km

2.
2(x-1)=a-x
2x-2=a-x
2x+x=a+2
3x=a+2
x=(a+2)/3

3(x-2)=a-x
3x-6=a-x
3x+x=a+6
4x=a+6
x=(a+6)/4

Then

(a+2) (a+6)
------- = --------
3 4

4*(a+2)=3*(a+6)
4a+8=3a+18
4a-3a=18-8
a=10