carnot engine A has an efficiency of $0\mathrm{.}50,$ and carnot engine B has an efficency of $0\mathrm{.}86.$ both engines uniltize the same hot reservoir, which has a temperature of $644$ K and delivers $1315$ J of heat to each engine. Find $($a$),($b$)$ the magnitude of the work produced by engine A and B respectively and $($c$),($d$)$ the temperatures of the cold reservoirs that they use.