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Emily sees a ship traveling at a constant speed along a straight section of a river. She walks parallel to the riverbank at a uniform rate faster than the ship. She counts 210 equal steps walking from the back of the ship to the front. Walking in the opposite direction, she counts 42 steps of the same size from the front of the ship to the back. In terms of emily's equal steps, what is the length of the ship?.

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onyebuchinnaji

In terms of Emily's equal steps, the length of the ship is 84.

  • Let the constant speed of the ship, = [tex]V_s[/tex]
  • Let the speed of Emily = V
  • let the length of the ship = d
  • let the time of Emily's motion, = t

Apply relative velocity formula for the forward and backward steps as follows;

Forward motion;

[tex](V - V_s )t = d\\\\(\frac{200}{t} - \frac{d}{t} ) t = d[/tex]

backward motion;

[tex](V + V_s) t = d\\\\(\frac{42}{t} + \frac{d}{t} ) t= d[/tex]

Solve the forward and backward motion together;

[tex](\frac{200}{t} - \frac{d}{t} )t = (\frac{42}{t} + \frac{d}{t} )t \\\\\frac{200}{t} - \frac{d}{t} = \frac{42}{t} + \frac{d}{t}\\\\\frac{200-42}{t} = \frac{d+ d}{t} \\\\2d = 168\\\\d = \frac{168}{2} \\\\d = 84[/tex]

Thus, in terms of Emily's equal steps, the length of the ship is 84.

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