Can someone help me with this question? please

9514 1404 393

  208

Step-by-step explanation:

First of all, it is useful to draw the factory location and the path the truck takes.

If you're paying attention, you will notice that the distance from each marked location to the origin is 3 grid squares horizontally and 4 grid squares vertically. This makes the distance to the origin be the hypotenuse of a 3-4-5 triangle, or 5 grid squares.

Then the distance diagonally from the warehouse to the airport is 10 grid squares. The distance horizontally from the airport to the factory is 6 grid squares, for a total distance of 10+6 = 16 grid squares.

You will notice the grid squares are marked as 13 miles each. The miles driven by the truck are ...

  (13 miles)(16) = 208 miles

_____

As you can see, it is helpful to notice when problems make use of 3-4-5 triangles.

If you want to compute this more or less directly, you can recognize the horizontal distance from warehouse to airport is 78 miles, and the vertical distance is 104 miles. The Pythagorean theorem tells you the diagonal distance is ...

 WA = √(78² +104²) = √16900 = 130

The distance to the factory is 78 miles, so the total is ...

  130 +78 = 208 . . . miles the truck drives

Explanation:

x is some positive number such that the earnings of Paul, Collin, and Brian are 2x, 3x and 4x in that order

The ratio 2x:3x:4x reduces to 2:3:4 when we divide all parts by x

The total amount of tips was 77.40 pounds

This means,

(Paul's Share)+(Collin's Share)+(Brian's Share) = Total Tips

(2x)+(3x)+(4x) = 77.40

9x = 77.40

x = 77.40/9

x = 8.6

Use that x value to find each of their share of tips

As a check, note how 17.20+25.80+34.40 = 77.40

The last step is to subtract the values for Brian and Paul

34.40 - 17.20 = 17.20

Brian earned £17.20 more in tips compared to Paul.