Question : A dog saw a cat at a distance of 280 m. The cat started running at the speed of 10 km/h and the dog also ran to catch it at the speed of 24 km/h. How much time will the dog take to catch the cat?
Option 1: 1.4 min
Option 2: 1.5 min
Option 3: 1.2 min
Option 4: 1.3 min
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Correct Answer: 1.2 min
Solution :
10 km/h = $\frac{25}{9}$ m/s
24 km/h = $\frac{20}{3}$ m/s
Relative speed = $\frac{20}{3}-\frac{25}{9} = \frac{60-25}{9} = \frac{35}{9}$
Now, the time taken to catch the cat by the dog
$= \frac{280}{ \frac{35}{9}}$
$= \frac{280 \times 9}{35}$
$=72$ seconds
$= \frac{72}{60} = 1.2$ min
∴ The dog will take 1.2 min to catch the cat.
Hence, the correct answer is 1.2 min.
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