Afire engine starts pumping water at 9: 20 am at the rate of 800 gallons per minute. another fire engine, pumping at the rate of 1000 gallons per minute, starts at 9: 30 am. at what time will the two engines have pumped the same number of gallons?

When they both pump, Engine #2 gains quantity over Engine #1 at the rate of 200 gallons per minute.

BUT ... when Engine #2 started up at 9:30, Engine #1 was already

           (800 x 10 minutes) = 8,000 gallons 

in the lead.  Engine #2 has to gain 8,000 gallons just to pull even.

Since Engine #2 gains 200 gallons per minute, it will take him

            (8,000) / (200) =  40 minutes   

to pull even with Engine #1.  

That moment will arrive at  (9:30 + 40 minutes)  =  10:10 AM .