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
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!