Do you understand how to find a ratio? Here are the answers to the questions above.
1) As the first distance is 6 miles and the second is 9 miles, the units cancel out and we have a ratio of six to nine, generally expressed as 6:9. Six and nine are both divisible by three, so we can reduce this to the simpler 2:3 ratio.
2) The ratio of her new salary to her old salary is 15:12 (the units, dollars, cancel out); these numbers are each divisible by three, so this reduces to 5:4. Expressed as a percentage, Mary received a 3/12 = 1/4 = 25% raise!
3) This is a tricky one! As the ratio is 1:4, we know that each side in triangle B is four times as long as the corresponding side in triangle A. As A is a right triangle, we calculate that 32 + 42 = 9 + 16 = 25 = 52, so z is 5. Five times four is twenty, means that the hypotenuse on triangle B must have length 20 (and the other two sides have lengths 12 and 16). 122 + 162 = 144 + 256 = 400, which is the square of 20, so the math checks out.