Question

A dog and a cat start running from the same corner around the rectangular garden.

Dog runs west and the cat runs north.

Cat's speed is $1$ meter per second faster than the dog's speed.

After $2$ seconds the distance between them is $10$ meters.

Find their speed in meters per second.

Answer 1

Use the formula of distance, speed time to calculate the speed of cat and dog:

Let the speed of dog be $x$ then the speed will be $x+1$ $\mathrm{m}/\mathrm{s}$.

It is given that the distance $10\mathrm{m}$ and time taken is $2$ seconds.

Therefore, total speed of cat and dog is,

$x+x+1=2x+1$.

Now, use the formula,

$$\begin{gathered} Speed=\frac{Dis\tan ce}{time} \\ \Rightarrow 2x+1=\frac{10}{2} \\ \Rightarrow (2x+1)=5 \\ \Rightarrow 2x=5-1 \\ \Rightarrow 2x=4 \\ \Rightarrow x=2 \end{gathered}$$

Hence, the speed of the dog is $2$ and the cat is $3$.