Answer : Cat will reach tree first.
Explanation :
It is given that,
Total distance between dog and tree is 30 yards. The cat has 10 yards lead. So, the distance between cat and tree is 20 yards.
Speed of cat is 6 Yards/ sec.
Speed of dog is 8 Yards/sec.
speed of cat is, [tex]S_c=\dfrac{distance\ covered\ by\ cat}{time\ taken}[/tex]
[tex]6\ Yards/sec=\dfrac{20\ Yards}{t_c}[/tex]
[tex]t_c=3.33\ sec[/tex]
Now, speed of dog is, [tex]S_d=\dfrac{distance\ covered\ by\ dog}{time\ taken}[/tex]
[tex]8\ Yards/sec=\dfrac{30\ yards}{t_d \ sec}[/tex]
[tex]t_d=3.75\ sec[/tex]
It is clear that, cat is taking less time as compared with dog. So, the cat will reach tree first.
The animal that will get to the tree first is the cat.
To know which animal will get to tree first, we shall determine the time taken for each animal to get to the tree. This can be obtained as follow:
Distance of cat to tree = 30 – 10 = 20 yard
Speed of cat = 6 yard/s
Time for cat to reach the tree =?
[tex]Time = \frac{Distance}{speed} \\\\ = \frac{20}{6}\\\\[/tex]
Thus, the time taken for the cat to get to the tree is 3.33 s
Distance of dog to tree = 30 yard
Speed of dog = 8 yard/s
Time for dog to reach the tree =?
[tex]Time = \frac{Distance}{speed}\\\\ = \frac{30}{8}\\\\[/tex]
Thus, the time taken for the dog to get to the tree is 3.75 s
Time for cat to reach the tree = 3.33 s
Time for dog to reach the tree = 3.75 s
From the calculations made above, we can see that the time taken for the cat to get to the tree is less compared to the time take for the dog to get to the tree.
Thus, we can conclude that the cat will get to the tree first.
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