Answer: He takes 24 seconds which represents change in time of his personal best after 200 yards .
Step-by-step explanation:
Since we have given that
Distance he covered by swimming = 25 yards
Time taken by him = 3 seconds
![\text{Speed of his swimming} =\frac{Distance}{Time}\\\\ \text{Speed of his swimming} =\frac{25}{3}](https://tex.z-dn.net/?f=%5Ctext%7BSpeed%20of%20his%20swimming%7D%20%3D%5Cfrac%7BDistance%7D%7BTime%7D%5C%5C%5C%5C%20%5Ctext%7BSpeed%20of%20his%20swimming%7D%20%3D%5Cfrac%7B25%7D%7B3%7D)
Now, if he covers 200 yards , the change of time will be
![\text{Time taken}=\frac{Distance}{Speed}\\\\\text{Time taken}=\frac{200}{\frac{25}{3}}\\\\\text{Time taken}=\frac{200\times 3}{25}\\\\\text{Time taken}=8\times 3\\\\\text{Time taken}=24 seconds](https://tex.z-dn.net/?f=%5Ctext%7BTime%20taken%7D%3D%5Cfrac%7BDistance%7D%7BSpeed%7D%5C%5C%5C%5C%5Ctext%7BTime%20taken%7D%3D%5Cfrac%7B200%7D%7B%5Cfrac%7B25%7D%7B3%7D%7D%5C%5C%5C%5C%5Ctext%7BTime%20taken%7D%3D%5Cfrac%7B200%5Ctimes%203%7D%7B25%7D%5C%5C%5C%5C%5Ctext%7BTime%20taken%7D%3D8%5Ctimes%203%5C%5C%5C%5C%5Ctext%7BTime%20taken%7D%3D24%20seconds)
Hence, he takes 24 seconds which represents change in time of his personal best after 200 yards .