It takes a man 20 minutes longer to travel from his home to his place of business if he drives at a rate of 30 mph than if he drives at a rate of 40 mph. How many miles is his home from his place of business?

20 minutes = 1/3 hours

let the distance be S

recall that time taken = distance/velocity

so, the time taken when travelling at 30 mph is S/30

and the time taken when travelling at 40 mph is S/40

therefore

S/30 - S/40 = 1/3

multiply through by 120

4S - 3S = 40

S = 40

distance = 40 miles