Question

Train a is 14 mph slower than train B. Train A travels 220 miles in the same time train B travels 290 miles. Find the speed of both trains

Answer 1

Recall your d = rt, distance = rate * time

if say train B has a speed of "r", then A has a speed of "r-14".

now, they each travelled those miles in the same time, say "t" hours.

$\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &-----&---&----\\ \textit{Train A}&220&r-14&t\\ \textit{Train B}&290&r&t \end{array} \\\\\\ \begin{cases} 220=t(r-14)\\ 290=rt\implies \frac{290}{r}=\boxed{t}\\ ----------\\ 220=\boxed{\frac{290}{r}}(r-14) \end{cases} \\\\\\ 220=\cfrac{290(r-14)}{r}\implies 220r=290r-4060\implies 4060=70r \\\\\\ \cfrac{4060}{70}=r\implies 58=r$

how fast is Train A?  well, r - 14.