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Free_Kalibri [48]
2 years ago
13

Train A and train B leave a central station at the same time. They travel the same speed, but in opposite directions, with train

A heading towards station A, and train B heading towards station B. Train A reaches station A after 212 h. Train B reaches station B after 4 h. Station A and Station B are 585 mi apart. What is the rate of the trains?
Mathematics
2 answers:
ratelena [41]2 years ago
8 0
Recall your d  = rt, distance = rate * time

so, keeping in mind that both trains are going at the same speed, say speed of "r" mph, after 212 hours A arrived at station A and after 4 hours, B arrived at station B.

now, the distance covered by train A is say "d", we know both stations are 585 miles apart, so, if train A covered "d" miles in those 212 hours, then train B covered the slack from 585 and d, that is "585 - d".

\bf \begin{array}{lccclll}
&\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\
&------&------&------\\
\textit{Train A}&d&r&212\\
\textit{Train B}&585 - d&r&4
\end{array}
\\\\\\
\begin{cases}
\boxed{d}=212r\\
585-d=4r\\
----------\\
585-\boxed{212r}=4r
\end{cases}
\\\\\\
585=216r\implies \cfrac{585}{216}=r\implies \cfrac{65}{24}=r\implies \stackrel{mph}{2\frac{17}{24}}=r
Marina86 [1]2 years ago
6 0

I just had the same question on a test and the answer was 90 MPH. Hope this helps somebody!

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