A biker traveling at his usual speed can go from his house to work in 4 hours. When the weather is bad, he travels 6 miles per hour slower, and it takes him half an hour more. How far is his work from his house?

Let d be the distance from his house.
Using the speed formula we have = distance / time
normlal speed - slower speed = 6 mph

d / 4 - 4/4.5 = 6
multiply the equation by 36, to cancel out the denominator.

36* d/4 - 36*d/4.5 = 36 (6)
Cancelling the denominators, we will only have:

= 9d - 8d = 216

= d = 216 miles to his house

check:

216 / 4 = 54 mph
216 / 4.5 = 48 mph
the difference is 6 mph