Since the father dug a hole with a rate of 4 feet per hour, if the father took 400 hours digging the hole, he dug a hole 4*400 = <<4*400=1600>>1600 feet deep.
Twice the depth of the hole that Michael's father dug is 2*1600 = <<2*1600=3200>>3200 feet
Michael wants to dig a hole 400 feet less than twice the depth of the hole that his father dug, meaning he wants to dig a hole 3200-400 = 2800 feet deep.
To dig a hole that is 400 feet less than twice as deep as his father's hole working at a rate of 4 feet per hour, Michael will have to work for 2800/4 = 700 hours.
#### 700