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Sagot :
ANSWER
75 mph
EXPLANATION
The first thing to note in the question is that the train spends the same amount of time travelling on level ground and in the mountains.
We have that the train travels 300 miles on level ground and 120 miles in the mountains.
Speed (rate of change) is given as:
[tex]R\text{ = }\frac{D}{t}[/tex]where D = distance and t = time
This means that on level ground:
[tex]R\text{ = }\frac{300}{t}[/tex]In the mountains:
[tex]R\text{ = }\frac{120}{t}[/tex]Recall that from the question, the rate of the train in the mountains is 30 mph.
This means that:
[tex]\begin{gathered} 30\text{ = }\frac{120}{t} \\ \Rightarrow\text{ t = }\frac{120}{30} \\ t\text{ = 4 hours} \end{gathered}[/tex]Since the time is the same in the two places, for level ground:
[tex]\begin{gathered} R\text{ = }\frac{300}{4} \\ R\text{ = }75\text{ mph} \end{gathered}[/tex]Therefore, the rate of the train on level ground is 75 mph.
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