High School

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------------------------------------------------ Lala is riding a motorcycle to Demak city with a speed of 50 km/hour. 8 km behind her, Poppy is driving a car moving at a speed of 80 km/hour. How long does it take Poppy to catch up with Lala?

A. 13 minutes
B. 15 minutes
C. 16 minutes
D. 18 minutes
E. 20 minutes

Answer :

To determine how long it takes for Poppy to catch up with Lala, we need to use the concept of relative speed.

Step-by-step Solution:

  1. Determine the Relative Speed:

    • Lala is traveling at 50 km/h.
    • Poppy is traveling at 80 km/h.
    • The relative speed of Poppy with respect to Lala is the difference in their speeds:
      [tex]80 \text{ km/h} - 50 \text{ km/h} = 30 \text{ km/h}[/tex]

  2. Determine the Distance Poppy Needs to Cover:

    • Initially, Poppy is 8 km behind Lala.
    • Therefore, Poppy needs to cover a distance of 8 km to catch up with Lala.

  3. Calculate the Time Required to Catch Up:

    • To find the time, use the formula:
      [tex]\text{Time} = \frac{\text{Distance}}{\text{Relative Speed}}[/tex]
    • Substitute the values:
      [tex]\text{Time} = \frac{8 \text{ km}}{30 \text{ km/h}}[/tex]
    • Simplifying the fraction:
      [tex]\text{Time} = \frac{8}{30} \text{ hours} = \frac{4}{15} \text{ hours}[/tex]

  4. Convert the Time from Hours to Minutes:

    • Since 1 hour is equal to 60 minutes, multiply the result by 60 to convert hours to minutes:
      [tex]\frac{4}{15} \text{ hours} \times 60 \text{ minutes/hour} = 16 \text{ minutes}[/tex]

Therefore, it takes Poppy 16 minutes to catch up with Lala. The correct answer is option C. 16 minutes.

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