Awork crew has a new pump and an old pump. the new pump can fill a tank in 5 hours, and the old pump can fill the same tank in 7hours. write and solve an equation for the time it will take both pumps to fill one tank if the pumps are used together?

The new pump fills 1/5 of the tank every hour, and the old one fills 1/7 of the tank per hour.  Thus, the fraction of the tank filled every hour is 1/5+1/7=12/35.  As a result, the tank will take 35/12 hours to fill completely (since 35/12*12/35 is one).

The first digit is in the middle school 100s place