Rory is playing a video game where each game lasts 13⁄4 hours. He wants to play for 9 hours today and this evening. How many games can he play?

A. 41⁄7

B. 6

C. 51⁄7

D. 52⁄5

Duration of each game playing = 1 3/4 hours.

Let us convert 1 3/4 into mixed fracions first.

1 3/4 = (1*4+3) / 4 = 7/4 hours.

Total number of hours Rory want to play = 9 hours.

Total number of games = Total number of hours : Duration of each game.

Plugging values, we get

Total number of games = 9 : 7/4.

Let us convert division sign into multiplication and flip the right side fraction, we get

9 * 4/7

Multiplying across, we get

(9*4) / 7 = 36/7.

Let us convert 36/7 into mixed fractions.

On dividing 36 by 7, we get quotient=5 and remainder=1.

So the answer 36/7 in fraction for will be 5 1/7.

Number of games Rory can play = 5 1/7 games.

Therefore, correct option is C. 5 1/7.