QuestionJonathan can play 3 hours for every 5 hours of work; Lucas can play 0.5 hours for every hour. Who plays more?

Studdy Solution

STEP 1

Assumptions1. Jonathan gets3 hours of video game time for every5 hours of homework or reading he completes. . Lucas gets30 minutes of video game time for every hour of homework or reading he completes.
3. Both boys spend the same amount of time on homework and reading.

STEP 2

First, we need to find the ratio of video game time to homework or reading time for both boys. For Jonathan, this is hours of video game time to5 hours of homework or reading time.
$Ratio_{Jonathan} = \frac{Video\, game\, time}{Homework\, or\, reading\, time} = \frac{}{5}$

STEP 3

For Lucas, this is30 minutes of video game time to1 hour of homework or reading time. To compare the ratios, we need to convert the minutes to hours.
$30\, minutes =0.5\, hours$

STEP 4

Now, we can find the ratio of video game time to homework or reading time for Lucas.
$Ratio_{Lucas} = \frac{Video\, game\, time}{Homework\, or\, reading\, time} = \frac{0.}{1}$

STEP 5

Now we compare the two ratios to find out who gets more video game time for the same amount of homework or reading time.
If $Ratio_{Jonathan} > Ratio_{Lucas}$ , then Jonathan gets more video game time.
If $Ratio_{Jonathan} < Ratio_{Lucas}$ , then Lucas gets more video game time.

STEP 6

Compare the ratios.
$\frac{3}{5} > \frac{0.5}{1}$ Jonathan's ratio is greater than Lucas's ratio, so Jonathan gets more video game time for the same amount of homework or reading time.
Jonathan gets more time playing video games.

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