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Consider a parallel-flow heat exchanger with area $A_p$ and a counter-flow heat exchanger with area $A_c$ . In both the heat exchangers, the hot stream flowing at $1 \: kg/s$ cools from $80^\circ C$ to $50^\circ C$. For the cold stream in both the heat exchangers, the flow rate and the inlet temperature are $2 \: kg/s$ and $10^\circ C$, respectively. The hot and cold streams in both the heat exchangers are of the same fluid. Also, both the heat exchangers have the same overall heat transfer coefficient. The ratio $A_c/A_p$ is _________
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