Question

Two buses leave at the same time traveling in opposite directions. One bus travels at 63mph and the other at 62mph. How soon will they be 187.5

miles apart?

Answer 1

recall your d = rt, distance = rate * time

the buses are traveling in opposite directions, but both are taking off at the same time
let's say bus A is going at 63mph and bus B is going at 62mph, so, we know their "r" rate for each

ok, after they had travelled for "t" time, they're both 187.5 miles apart, at that instant, bus A has been travelling for "t" hours and bus B has been also travelling for "t" hours as well

now, if bus A covered say "d" miles in those "t" hours, then bus B covered the slack from 187.5 and "d", or 187.5 - d

thus


`\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ \textit{bus A}&d&63&t\\ \textit{bus B}&187.5-d&62&t \end{array} \\\\\\ \begin{cases} \boxed{d}=63t\\ 187.5-d=62t\\ ----------\\ 187.5-\boxed{63t}=62t \end{cases}`

solve for "t".