Question

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?

Answer 1

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".

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

Answer 2

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