A fox called Fred spots a rabbit happily nibbling grass 18 meters away. At the same moment, the rabbit (called Roger) notices the Fox.
The fox chases the rabbit who runs in a straight line away from him.
Fred can run at $5\dfrac{1}{2}$ meters a second.
Roger can run $3\dfrac{1}{2}$meters a second.
How long will it take the fox to catch up with the rabbit?

Hint: Find the relative speed of the fox and the rabbit and then use the formula given below to find the time taken:
Time taken$ = \dfrac{{\left( {{\text{Distance between them}}} \right)}}{{{\text{Relative speed}}}}$
It is given that a fox spotted a rabbit that was happily nibbling grass 18meters away from the fox. At the same moment, the rabbit (called Roger) notices the Fox. It is also given that Fred can run at $5\dfrac{1}{2}$ meters a second and Roger can run $3\dfrac{1}{2}$meters a second.
We have to find the time taken by the fox to catch up with the rabbit.
Speed of fox$ = 5\dfrac{1}{2}$ meter per second
Speed of rabbit$ = 3\dfrac{1}{2}$ meter per second
First, find the relative speed of fox and rabbit by taking the difference in their speed.
As we have given, speed of the fox is faster than the speed of the rabbit, and then their relative speed is given as:
The Relative speed of fox and rabbit$ = \left( {{\text{Speed of fox}}} \right) - \left( {{\text{Speed of rabbit}}} \right)$
Substitute the speeds of fox and the rabbit in the above equation:
The Relative speed of fox and rabbit$ = \left( {5\dfrac{1}{2}} \right) - \left( {3\dfrac{1}{2}} \right)$
The Relative speed of fox and rabbit$ = \dfrac{{11}}{2} - \dfrac{7}{2}$
The relative speed of fox and rabbit$ = \dfrac{4}{2}$
The relative speed of fox and rabbit$ = 2$
So, the relative speed of the fox and the rabbit is 2 meters per second.
Then, the time taken by the fox to catch up the rabbit is given as:
Time taken$ = \dfrac{{\left( {{\text{Distance between them}}} \right)}}{{{\text{Relative speed}}}}$
Substitute the values in the above equation:
Time taken$ = \dfrac{{\left( {18} \right)}}{2}$
Time taken$ = 9$
Therefore, the fox will take 9 seconds to catch up with the rabbit.

Note: We have to find the difference in the speed of two objects if the speed of the first object is larger than the second object then take the difference of the speed of the first object to the second object and vise-versa.