Question

A train travels 300 miles on level ground in the same amount of time it travels 120 miles in the mountains. The rate of the train in the mountains is 30 mph. Find the rate of the train on level ground.(I just need an explanation on how to do this problem, or at least an equation. I can solve it once I have an equation)

Answer 1

75 mph

Step-by-step 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:

`R\text{ = }(D)/(t)`

where D = distance and t = time

This means that on level ground:

`R\text{ = }(300)/(t)`

In the mountains:

`R\text{ = }(120)/(t)`

Recall that from the question, the rate of the train in the mountains is 30 mph.

This means that:

`\begin{gathered} 30\text{ = }(120)/(t) \\ \Rightarrow\text{ t = }(120)/(30) \\ t\text{ = 4 hours} \end{gathered}`

Since the time is the same in the two places, for level ground:

`\begin{gathered} R\text{ = }(300)/(4) \\ R\text{ = }75\text{ mph} \end{gathered}`

Therefore, the rate of the train on level ground is 75 mph.