during morning rush, entering travelers can fill a station in 20 min.departing trains can empty it in 30 min. At rush hour pace, how l

Question

during the morning rush, entering travelers can fill a station in 20 minutes. Fortunatley, departing trains can empty it in 30 minutes. At rush hour pace, how long will it take to for the station to fill with travelers

Answer 1

Fill station in 20 minutes  ==>  in 1 minute 1/20 of station will be filled  

Empty station in 30 minutes  ==>  in 1 minute 1/30 of station will be emptied  

 

In 1 minute (1/20 - 1/30) will be the net change in fullness of the station  

(Note the minus sign to indicate emptying) 

 

In T minutes the net change will be T*(1/20 - 1/30) 

 

The station will be full when 

 

T*(1/20 - 1/30) = 1 

T*(3/60 - 2/60) = 1

T*(1/60) = 1

T = 60 minutes 

 

Check:  In 60 minutes the station will be filled 60/20 = 3 times and  

            emptied 60/30 = 2 times for a net change of 1 complete filling