I'm really struggling with word problems right now. Got through 20 just three left. Can someone please give me some pointers or the first few steps?

1. A sum of money is divided between A, B and C in the ratio 1 : 2 : 3. However, before the
money is divided C dies and it is decided to divide his share between A and B in the
ratio 1 : 3. If After C’s share is divided B has $2000 more than A, how much money was
there altogether?

2. Rectangles A and B are both four times as long as they are wide and the length of
rectangle A is three times the length of rectangle B. If the difference in the perimeters
is 16 cm, find the dimensions of each rectangle.

3. A certain journey took 40 min to complete.
If half the distance was travelled at an average
speed of 100 km/h and the other half at an
average speed of 60 km/h, what was the
length of the journey?

1. original amounst

A = x, B = 2x, C = 3x
After the death,
A has x + (1/4)(3x) = 7x/4
B has 2x + (3/4)(3x) = 17x/4

B-A = 2000
17x/4 - 7x/4 = 2000
17x - 7x = 8000
10x = 8000
x = 800

take it from there

2. Start with the smallest rectangle
small-width = x
small-length = 4x

large-width = 3x
large-length = 12x

large per = 30x
small per = 10x

Can you finish it?

3. let the length of the journey be 2x
so x/100 + x/60 = 40/60

its all yours .....

Sure! I can help you with these word problems by providing you with some pointers and explaining the steps to solve them. Let's go through each problem one by one:

1. In this problem, we need to determine the total sum of money that was divided between A, B, and C. We are given that the original ratio of their shares is 1:2:3. However, C dies, and his share is then divided between A and B in the ratio 1:3.

To start solving this problem, we can assume a common variable to represent the total sum of money. Let's call it "x."

Now, according to the given information, the shares of A, B, and C would be (1/6)x, (2/6)x, and (3/6)x respectively.

Next, we are told that after C's share is divided, B has $2000 more than A. This means that the share of B is $2000 more than the share of A.

We can set up an equation to represent this situation:
(2/6)x - (1/6)x = $2000

Simplifying the equation gives us:
(1/6)x = $2000

To find the value of "x," we can multiply both sides of the equation by 6:
x = $12,000

Therefore, the total sum of money was $12,000.

2. For this problem, we are given two rectangles, A and B. They have different dimensions, but their lengths are related. Rectangle A is three times the length of rectangle B, and both rectangles are four times as long as they are wide.

To solve this problem, we can start by assigning variables to the dimensions of the rectangles. Let's say the width of both rectangles is "w."

The length of rectangle A would be 4w, as it is four times as long as its width.

The length of rectangle B would then be (1/3) * 4w = (4/3)w, as it is three times less than the length of rectangle A.

Now, we are given that the difference in the perimeters of the two rectangles is 16 cm.

The perimeter of a rectangle is calculated by adding all four sides.

So, we can set up an equation to represent the given information based on the calculated dimensions:
2(4w + w) - 2((4/3)w + w) = 16 cm

Simplifying the equation gives us:
8w + 2w - (8/3)w - 2w = 16 cm
(6/3)w = 16 cm
2w = 16 cm
w = 8 cm

Substituting the value of "w" back into the dimensions, we find:
The dimensions of rectangle A are 4w = 4 * 8 = 32 cm by 8 cm
The dimensions of rectangle B are (4/3)w = (4/3) * 8 = 32/3 cm by 8 cm

Therefore, the dimensions of rectangle A are 32 cm by 8 cm, and the dimensions of rectangle B are 32/3 cm by 8 cm.

3. In this problem, we are given a certain journey that took 40 minutes to complete. The journey was divided into two equal halves, with one half traveled at an average speed of 100 km/h and the other half at an average speed of 60 km/h.

To find the length of the journey, we can first calculate the time taken for each half.

Since the journey is divided into equal halves, each half took 40/2 = 20 minutes or 1/3 hour to complete.

Let's assume the length of the journey is "d" km.

The time taken for the first half is d/2, and the time taken for the second half is also d/2.

We can now set up an equation based on the given information:
(d/2) / 100 + (d/2) / 60 = 1/3

Simplifying the equation gives us:
3d/200 + 5d/600 = 1/3
9d/600 + 5d/600 = 1/3
14d/600 = 1/3

To solve for "d," we multiply both sides of the equation by 600/14:
d = (600/14) * (1/3)

Simplifying further, we find:
d ≈ 14.29 km

Therefore, the length of the journey is approximately 14.29 km.

I hope these explanations and steps help you in solving your word problems. Let me know if you need any further assistance!