How many hours did he play outdoors?

[anonomous]

suppose that a child's hours of outdoor play are inversely proportional to that child's hours of television.Last week, nine-year-old james played outdoors a total of 20 hours and watched 8 hours of TV This week he only watched 3 hours of TV. How many hours did he play outdoors?

 

[notthejake]

let o = hours of outdoor play and t = hours of television

for inverse proportions, o = k / t, or o*t = k (a constant)
in other words, as one goes up, the other goes down

we know that when o = 20 then t = 8 ==> o * t = 160 = k

so o * t = 160

if t = 3, then o = 160 / 3 = 53.3

he played outside for 53.3 hours (53 hours and 20 minutes)
(good, turn off the x-box!)