Question

An express train travels 200miles between two cities. During the first 108miles of a trip, the train traveled through mountainous terrain . The train traveled 10miles per hour slower through mountainous terrain than through level terrain. if the total time travel between the cities was 5hours, find the speed of the train on level terrain

Answer 1

Given:

An express train travels 200miles between two cities.

Let, s be the train speed in level terrain.

(s-10) be the speed in the mountains.

The distance on level terrain is 200-108=92 miles

The equation becomes,

`\begin{gathered} Time=\frac{Dis\tan ce}{\text{sped}} \\ (108)/(s-10)+(92)/(s)=5 \end{gathered}`

Solve the equation,

`\begin{gathered} (108)/(s-10)+(92)/(s)=5 \\ (100s+92(s-10))/(s(s-10))=5 \\ 108s+92s-920=5s^2-50s \\ 5s^2-250s+920=0 \\ s^2-50s+184=0 \\ s^2-46s-4s+184=0 \\ s(s-46)-4(s-46)=0 \\ (s-46)(s-4)=0 \\ \Rightarrow s=46,4 \end{gathered}`

But he appropriate value of s should be 46.

Since for s=4, s-10=-6 that is not possible.

So, the speed of the train on level terrain is 46 mph