Mathematics

Question

Youssef can either way from his home to his workplace or ride his bicycle. he walks at a pace of 1 block per min, but he can travel 1 block in 20 sec on his bicycle. if it takes youssef 10 min longer to walk to work than to ride his bike, how many blocks away from work does he live ?‚Äč

1 Answer

  • Youssef lives 15 blocks away from his work

    Solution:

    Given that Youssef can either way from his home to his workplace or ride his bicycle

    Let "x" be number of blocks away from work Youssef works

    Case 1: walking

    He walks at a pace of 1 block per min

    Therefore,

    1 block = 1 minute

    Thus to cross "x" blocks he takes "x" minutes

    Case 2: Bicycle

    He can travel 1 block in 20 sec on his bicycle

    We know that,

    To convert seconds to minute, divide the time value by 60

    [tex]\rightarrow 20 seconds = \frac{20}{60} minutes = \frac{1}{3} minutes[/tex]

    Thus he takes 1/3 minutes for 1 block

    So to cross "x" blocks he will take [tex]\frac{x}{3}[/tex] minutes

    Given that it takes youssef 10 min longer to walk to work than to ride his bike

    This means difference between time taken to cross "x" blocks by walking and ride by bicycle is 10 minutes

    [tex]\rightarrow x - \frac{x}{3} = 10\\\\\rightarrow \frac{3x - x}{3} = 10\\\\\rightarrow \frac{2x}{3} = 10\\\\\rightarrow x = \frac{30}{2}\\\\\rightarrow x = 15[/tex]

    Thus he lives 15 blocks away from his work

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