Question

Two trains are 400 miles apart, and their speeds differ by 10 mph. They travel toward each other and meet in 4 hours. Find the speed of each train.

Answer 1

So.. the two trains, are 400 miles apart, their speeds differ by 10, so one train is faster than the other.. .let's say   train A is faster than train B, by 10mph

so if train A has a speed rate of "r", then B has a rate of "r - 10"

after train A has beeng running for 4hrs, it has travelled a distance "d"

train B has travelled also for 4hrs, they're both 400 miles apart, and travelling towards each other, so the total distance travelled by both is 400miles

so after 4hours B has travelled the slack from 400 and "d", namely 400 - d

recall your d = rt --> distance = rate * time

$\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ \textit{Train A}&d&r&4\\ \textit{Train B}&400-d&r-10&4 \end{array}\\\\ -----------------------------\\\\ \begin{cases} \boxed{d}=4r\\ 400-d=(r-10)4\\ ----------\\ 400-\boxed{4r}=(r-10)4 \end{cases}$

solve for "r", to find the speed of the faster train A

what's the speed of B? well, B's rate is r - 10