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algebra help asap

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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?

Nov 11, 2021

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What is the length of the ship?

Hello Guest!

$$\ v_{sh}\cdot t+L_{sh}\ =210\ steps\\ \underline{-v_{sh}\cdot t+L_{sh}=42\ steps}$$

$$2\cdot L_{sh}=252\ steps$$

$$L_{sh}=126\ steps$$

The length of the ship is 126 steps from Emily.

!

Nov 11, 2021
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this is from the amc 10a

Nov 11, 2021
edited by Guest  Nov 11, 2021
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Lets Assume, Veocity of Emily is 1 step per second.

Forward Journey:

Emily Travels 210 Steps, The Ship travels 210 - Lsh

Time taken in both cases 210 Sec. /

Hence: Vsh * 210 =  210 - Lsh

==> Vsh  = 1 - (Lsh/ 210)

Reverse Journey:

As usual She takes 42 steps in 42 sec.

At 42nd Step she reached the other end of the ship, so the Ship Travels (Lsh  - 42 ) steps

Again: Vsh = (Lsh  - 42 ) / 42 =  (Lsh/ 42 ) - 1

1 - (Lsh/ 210) = (Lsh/ 42 ) - 1

Result Lsh = 70 Steps

Thanks

Krishna Korukonda

Nov 11, 2021
edited by Guest  Nov 11, 2021