RB_CH02_Q023. 100-day call IV increases by 25 - effect on one-day IV

You hold a 100-day European call option on a stock with implied volatility 20. Suppose that you know now right now what implied volatility will increase to 25, but that after that it will return to 20 for the remainder of its life. What extension to the life of the call would produce the same change in the present value of the call as the above-mentioned single-day increase in volatility (assuming a constant implied volatility at 20)? That is, other things being equal, what change in the term to maturity is equivalent to the quoted one-day change in the implied volatility? Explain carefully.