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June can run 6 laps in x minutes. Miri...

June can run 6 laps in x minutes.
Miriam can run 11 laps in 2x minutes.
`{:("Quantity A","Quantity B"),("The number of minutes it","The number of minutes it"),("takes june to run 24 laps","takes Mirian to run 22 laps"):}`

A

Quantity A is greater.

B

Quantity B is greater.

C

The two quantities are equal.

D

The relationship cannot be determined from the infromation given.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we will calculate the time taken by June to run 24 laps and the time taken by Miriam to run 22 laps, and then compare the two quantities. ### Step 1: Calculate the time taken by June to run 24 laps - June can run 6 laps in \( x \) minutes. - Therefore, the time taken by June to run 1 lap is: \[ \text{Time per lap for June} = \frac{x}{6} \text{ minutes} \] - To find the time taken by June to run 24 laps, we multiply the time per lap by 24: \[ \text{Time for 24 laps} = 24 \times \frac{x}{6} = \frac{24x}{6} = 4x \text{ minutes} \] ### Step 2: Calculate the time taken by Miriam to run 22 laps - Miriam can run 11 laps in \( 2x \) minutes. - Therefore, the time taken by Miriam to run 1 lap is: \[ \text{Time per lap for Miriam} = \frac{2x}{11} \text{ minutes} \] - To find the time taken by Miriam to run 22 laps, we multiply the time per lap by 22: \[ \text{Time for 22 laps} = 22 \times \frac{2x}{11} = \frac{44x}{11} = 4x \text{ minutes} \] ### Step 3: Compare the two quantities - From our calculations, we found that: - Time taken by June to run 24 laps = \( 4x \) minutes - Time taken by Miriam to run 22 laps = \( 4x \) minutes - Therefore, we can conclude that: \[ \text{Quantity A} = \text{Quantity B} \] ### Final Answer Both quantities are equal.
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