Phone battery

Mrs. Helen has an old cell phone with nothing to do but makes phone calls. The cell phone will discharge in 72 hours when fully charged and on the phone. Three hours of calling in a row are enough to discharge a fully charged phone.
After the last full charge, Mrs. Helen first called her daughter for 25 minutes, then did not use it for 24 hours, then had a 45-minute call with her granddaughter, and then called her girlfriend. After how many minutes of talking to her girlfriend, did her phone go blank?

Final Answer:

t =  50 min

Step-by-step explanation:

$$\begin{gathered} v_1=1/(72\cdot 60)=\frac{1}{4320}\doteq 0.0002 \\ {v}_2=1/(3\cdot 60)=\frac{1}{180}\doteq 0.0056 \\ 25\cdot v_2+24\cdot 60\cdot v_1+45\cdot v_2+t\cdot v_2=1 \\ a=25\cdot v_2+24\cdot 60\cdot v_1+45\cdot v_2=25\cdot 0.0056+24\cdot 60\cdot 0.0002+45\cdot 0.0056=\frac{13}{18}\doteq 0.7222 \\ a+t\cdot v_2=1 \\ t=(1-a)/v_2=(1-0.7222)/0.0056=50\text{min} \end{gathered}$$

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