Question

Two planes fly in opposite directions. One travels 400 mi/h and the other 600 mi/h. How long will it take before they are 4,000 mi apart?

Answer 1

recall your d = rt, distance = rate * time.

A = first plane

B = second plane

the assumption is that they both start off from the same point at the same time in opposite directions.

at some time say "t" hours, plane A will be some distance, hmmm say "d" miles, since we know they'll both be 4000 miles apart, then plane B will be "4000 - d" miles at that time, since both took off at the same time, then plane A as well as plane B have both been travelling "t" hours.

$\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{plane A}&d&400&t\\ \textit{plane B}&4000-d&600&t \end{array}\qquad \qquad \begin{cases} \boxed{d}=400t\\\\ 4000-d=600t \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 2nd equation}}{4000-\boxed{400t}=600t}\implies 4000=1000t\implies \cfrac{4000}{1000}=t\implies 4=t$