Let the raw water flow be 1, the pump discharge per hour be x, and the rain increment be y, and the equation can be listed:

1) (x-y)* 10= 1

2) (2x-y)*3= 1

According to 1), y = x-110 is obtained.

Substituting 2) gives 2x-x+110 =1/3.

Calculate x =1/3-110 = 7/30; y = 7/30- 1/ 10 = 2/ 15

Therefore, the time required to start the three pumps is t =1(3x+y) =1/(21/30+4/30) = 6/5.

It takes 1 hour 12 minutes.