Tom reads at an average rate of 30 pages per hour, while Jane reads at an average rate of 40 pages per hour. If Tom starts reading a novel at 4: 30 and Jane begins reading an identical copy of the same book at 5: 20, then at what time will they be reading the same page?
Answer
Answer (as printed):
Explanation
Suppose they are reading the same page $x$ hours after 5: 20. $$\begin{aligned} & \text { Time from } 4: 30 \text { to } 5: 20=50 \min =\frac{5}{6} \mathrm{hr} \text {. } \\ & \text { Then, } 30\left(x+\frac{5}{6}\right)=40 x \Leftrightarrow 30 x+25=40 x \Leftrightarrow 10 x=25 \Leftrightarrow x=2.5 \text {. } \end{aligned}$$ Hence, Tom and Jane will be reading the same page $2 \frac{1}{2} \mathrm{hrs}$ i.e., 2 hr 30 min after 5: 20 i.e., at 7: 50.
Explanation as extracted from the printed page; notation may be imperfect.