2024 Cayley Problem 20

Jiwei and Hari entered a race. Hari finished the race in \frac{4}{5} of the time it took Jiwei to finish. The next time that they raced the same distance, Jiwei increased his average speed from the first race by x\%, while Hari maintained the same average speed as in the first race. In this second race, Hari finished the race in the same amount of time that it took Jiwei to finish. The value of x is

\textbf{(A)}\ 20\quad \textbf{(B)}\ 25\quad \textbf{(C)}\ 35\quad \textbf{(D)}\ 40\quad \textbf{(E)}\ 50

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.