Solve this proportion problem or can you?

Question

Please answer and show work on how you did it. Jonathan's parents told him that for every 6 hours of homework or reading he completes, he will be able to play 4 hours of video games. His friend Lucas's parents told him that he can play video games for 45 minutes for every hour of homework he completes. If both boys spend the same amount of time on homework and reading this week, which boy gets more time playing video games and by how much more?

Answer 1

Jonathan

 

homework          video games

  6 hours                4 hours

 

Lucas

 

homework          video games

  1 hour                 3/4 hour    (45 minutes=45/60=3/4)

 

Jonathan has to do homework for 6 hours before playing video games.

If Lucas does 6 hours of homework he plays video games for 6*(3/4)=18/4=4.5 hours

Lucas plays video games longer by 0.5 hours

if you need a proportion...

Jonathan is 6 hr/4 hr

Lucas is 1 hr/(3/4)

1/(3/4)=6/x where x=# of hours playing video games

cross multiply (one solution for solving)

1(x)=6(3/4)

x=18/4=4.5 hours again

 

 

Answer 2

For 6 hours work, Jonathan gets 4 hours videos.

For 1 hour work, Jonathan gets 4/6 hours, or 2/3 hour, or 40 minutes.

 

That is 5 minutes less than Lucas gets for working one hour.