Explanation

A train travels s miles in t hours, hence speed of the train = \(\frac{s}{t}\) miles/hours.

Number of hours will the train travel y miles = \(\frac{distance}{speed}=\frac{yt}{s}\).

Hence option C is correct.
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In case the above post isn't clear enough here it is broken down:

First I changed the S & T because it's confusing when using speed equations where usually S = speed (probably could keep T for Time, but I digress)

Speed equations:
Speed = \(\frac{distance}{time} \) Time= \(\frac{distance}{speed}\) Distance = \(\frac{speed}{time}\)

Changed variables: S--> M (miles) T--> H (hours) D2 --> Y

Speed = M/H

Problem: If the train travels "M" miles in "H" hours, in how many hours will the train travel Y(D2) miles?

Find H:

Time= \(\frac{distance}{speed} \)

(Plug variables)

Distance = Y

Speed = \(\frac{distance}{time}\) ---> \(\frac{M}{H
}\)

Time --> Y/(\(\frac{M}{H}\)

Remember, DIVISION of a fraction = multiplication of reciprocal

So:

Y/(\(\frac{M}{H}\)) = \(\frac{Y}{1}\) * \(\frac{H}{M}\) = \(\frac{YH}{M}\)



Replace the variables:

\(\frac{YH}{M}\) = \(\frac{YT}{S}\)


Option C


Tah dahhh