1. The best way to start is to figure out what you need to find out, what information you have to get there, and then visually work your way through. There's 2 parts to the question:

What you need to find out: How many hours the car drove at each speed - 75 km/h and 110 km/h

What you're given: Total hours the trip took - 5.9

Since we don't have the hours @ each speed, we can fill in variables to visually work through it.

X = 75 km/h and Y = 110 km/h

**X + Y = 5.9**

The other piece is using the rest of the information they gave. Knowing that distance = speed x time, we can make the formula:

**600 km/h = D1 + D2**

We can fill in more with the rest of the information given & with the distance formula we know D1 = 75 x time and D2 = 110 x time.

**600 km/h = (75 x Time) + (110 x Time)**

We already created a time formula above, X + Y = 5.9 so we can add this to our second one

**600 km/h = 75X + 110Y**

We can fill in the blanks with our resources by flipping them around.

If 2 + 3 = 5, then 5 - 2 = 3

Same goes for X + Y = 5.9, that means 5.9 - X = Y. Now we have enough information to add to the formula and work our way through

**600 km/h = 75X + 110(5.9 - X)**

**600 km/h = 75x + 649 - 110X**

**49=35X**

**X=1.4**

If X=1.4, then to find Y we'll use X + Y = 5.9 again.

**1.4 + Y = 5.9**

**Y = 4.5**

**She drove 1.4 miles ( X ) at 75 km/h and 4.5 miles ( Y ) at 110 km/h.**

**2. Start with what you're given again (28m) and map out what you need to find.**

Width can = X and Length = Y, so you can start with

X + Y = 28m, but because there's 4 sides (2 lengths and 2 widths) it will be

2X + 2Y = 28

Now the rules tell us that the length = twice the width, minus 1

2X - 1 = Y, so we can plug this into our first given formula as:

2X + 2(2X - 1) = 28

2X + 4X - 2 - 28 = 0

2X + 4X - 30 = 0

6X - 30 = 0

X = 5

Now that we know that X = 5, we can fill it into our original formula to find Y

2(5) + 2Y = 28

10 + 2Y = 28

2Y = 18

Y = 9

The length of the lawn (9m) is 1m less than twice the width (5m).

9 = (5 x 2) - 1

Since we walked through the first 2, I'm going to let you try #3 to find out how much a hamburger and a cheeseburger cost. :) Good luck!

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## Comments

2. Start with what you're given again (28m) and map out what you need to find.

Width can = X and Length = Y, so you can start with

X + Y = 28m, but because there's 4 sides (2 lengths and 2 widths) it will be2X + 2Y = 28Now the rules tell us that the length = twice the width, minus 1

2X - 1 = Y, so we can plug this into our first given formula as:2X + 2(2X - 1) = 282X + 4X - 2 - 28 = 02X + 4X - 30 = 06X - 30 = 0X = 5Now that we know that X = 5, we can fill it into our original formula to find Y

2(5) + 2Y = 2810 + 2Y = 282Y = 18Y = 9The length of the lawn (9m) is 1m twice the width (5m).

9 = (5 x 2) - 1Since we walked through the first 2, I'm going to let you try #3 to find out how much a hamburger and a cheeseburger cost. :) Good luck!