Mathematics

Question

Scott likes to run long distances. He can run 20 km in 85 minutes. He wants to know how many minutes (m) it will take him to run 52 km at the same pace.
Which proportion could Scott use to model this situation?
Please choose from one of the following options.

m/20=85/52

m/85=52/20

Solve the proportion to determine how long it will take Scott to run 52 km.

2 Answer

  • Answer:

    m/85=52/20 is the correct answer.

    To solve, cross multiply and solve for m.

    20m=4,420

    m=221

    It will take 221 minutes.

  • The model required to find the time it takes to run 52 km is needed.

    The required proportion is [tex]\dfrac{m}{85}=\dfrac{52}{20}[/tex]

    Scott will take 221 minutes to run 52 km.

    Distance Scott runs is 20 km.

    Time taken to run 20 km is 85 minutes.

    Time taken to run 52 km is needed

    If the same pace is maintained this means the speed will be equal of both the runs.

    Let m be the minutes taken to cover 52 km

    [tex]\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]

    Speed of Scott's first run

    [tex]\dfrac{20}{85}[/tex]

    Speed of Scott's next run

    [tex]\dfrac{52}{m}[/tex]

    Since, the speeds are equal

    [tex]\dfrac{20}{85}=\dfrac{52}{m}\\\Rightarrow \dfrac{m}{85}=\dfrac{52}{20}[/tex]

    So, the required proportion is [tex]\dfrac{m}{85}=\dfrac{52}{20}[/tex]

    Solving it

    [tex]m=\dfrac{52}{20}\times 85=221\ \text{minutes}[/tex]

    Hence, Scott will take 221 minutes to run 52 km.

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