charlie leaves home going 40 miles per hour. When charlie is 9 miles from home, Danny starts after charlie from the same place, going 55 miles per hour. How long does it take Danny to catch up charlie?

Let h be the number of hours that pass when Charlie starts. We have the following equations: Charlie: D = 40h + 9 Danny: D = 55h Set them equal to each other: 40h + 9 = 55h Subtract 40h from both sides: 15h = 9 h = 3/5 3/5 of an hour = 3(60)/5 = 36 minutes