The father is 60 years old and his son is half his age. how old was the boy when his father was 4 times his age?

Let y = years ago when dad's age was 4 times son's age

60-y=4 (30-y)

60-y=120-4y

-y+4y=120-60

3y=60

y=60/3

y = 20 years ago

Then 30-20 = 10 yrs. old, the boys age when his dad was 40 years old.