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John steps on an escalator to leave a subway. Then, 5 seconds later, Jane steps on a parallel escalator to enter the subway. They pass 15 seconds after that. If both escalators are travelling at a speed of 6 feet per second, what is the length â„“ of the escalators

Respuesta :

Answer:

[tex]L = 210 ft[/tex]

Explanation:

velocity of the Escalators is given as 6 ft/s

now we know that Jane steps on parallel escalator after t = 5 s

so distance moved by John in same time interval is given as

[tex]d = v t[/tex]

[tex]d_1 = 6 \times 5[/tex]

[tex]d_1 = 30 ft[/tex]

now John and Jane will move towards each other with relative speed

[tex]v_r = 6 + 6 = 12ft/s[/tex]

Then will approach towards each other with this relative speed and meet after t = 15 s

so the distance moved by them

[tex]d = v_r \times t[/tex]

[tex]d_2 = 12 \times 15 [/tex]

[tex]d_2 = 180 ft[/tex]

so total length of the escalators is given as

[tex]L = d_1 + d_2 [/tex]

[tex]L = 30 + 180[/tex]

[tex]L = 210 ft[/tex]

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