A mathematician works for t hours per day and solves p problems per hour, where t and p are positive integers and 1 < p < 20. One day, the mathematician drinks some coffee and discovers that he can now solve 3p + 1 problems per hour. In fact, he only works for t - 4 hours that day, but he still solves twice as many problems as he would in a normal day. How many problems does he solve the day he drinks coffee?
