Question

Two cars leave the origin; one goes north at 45 mph and the other goes south at 40 mph. after how many hours will they be 350 miles apart?

Answer 1

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

so, say car N goes north at 45mph, and car S goes south at 40mph.

after "some time" they'd be apart 350 miles, when that happens, N has been travelling for say "t" hours, and S has been travelling for the same "t" hours, their time has to be the same.

now, we know they'd be 350 miles apart, so if say N has gone "d" miles, then S has gone the slack, or "350 - d".

and we know their rates.


`\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ \textit{Car N}&d&45&t\\ \textit{Car S}&350-d&40&t \end{array} \\\\\\ \begin{cases} \boxed{d}=45t\\ 350-d=40t\\ --------\\ 350-\boxed{45t}=40t \end{cases} \\\\\\ 350=85t\implies \cfrac{350}{85}=t\implies \cfrac{70}{17}=t\implies 4(2)/(17)=t`

which is about 4 hours and 7 minutes with 3.5 seconds.