Question

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?

Answer 1

let d be the distance from his house

From the information we can say "He takes 4 hours normally, but 4.5 hrs in bad weather"

Write a speed equation; speed = dist/time

normal speed - slower speed= 6 mph

d/4 - d/4.5 = 6

multiply equation by 36 to get rid of the denominators

36*d/4 - 36*d/4.5 = 36(6)

Cancel the denominators

9d - 8d = 216

d = 216 mi to his house

Answer 2

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