jmc

Initially, the difference between the water temperature and the room temperature is $212-68=144$ degrees Fahrenheit. After $5$ minutes, the difference between the temperatures is $144÷2=72$ degrees Fahrenheit. After $10$ minutes, the difference between the temperatures is $72÷2=36$ degrees Fahrenheit. After $15$ minutes, the difference between the temperatures is $36÷2=18$ degrees Fahrenheit. At this point, the water temperature is $68+18=\boxed{86}$ degrees Fahrenheit. Remark Alternatively, we can condense the solution above into the following equation: $$68+(212-68)\cdot {\left(\frac{1}{2}\right)}^{\frac{15}{5}}=86.$$