Answer:
The dog and the cat will meet at E.
Step-by-step explanation:
We can find the point where both the dog and the cat meet by finding the total of the path, then use the comparison method.
The total length of the path = 4 + 3 + 1 + 2 + 1 + 1 + √2 + √2 + √2 + √2 + 4
= 16 + 4√2
Since the dog walks 3 times as fast as the cat, then the comparison:
dog's distance : cat's distance : total distance = 3 : 1 : (3 + 1)
= 3 : 1 : 4
Now we can find either dog's distance or cat's distance using the comparison. Since the cat's distance is shorter, it will be faster to calculate its distance.
cat's dist. : total dist. (in part) = cat's dist. : total dist. (in units)
1 : 4 = cat's dist. (in units) : (16 + 4√2)
[tex]\displaystyle cat's\ distance=\frac{1(16+4\sqrt{2}) }{4}[/tex]
[tex]\displaystyle =\frac{4(4+\sqrt{2}) }{4}[/tex]
[tex]\bf=4+\sqrt{2}[/tex]
* Distance from Q to E = 4 + √2 ⇒ E is correct
