Question

Two cars leave the same location traveling in opposite directions. One car leaves at 3:00 p.m. traveling at an average rate of 55 mph. The other car leaves at 4:00 p.m. traveling at an average rate of 75 mph. How many hours after the first car leaves will the two cars be 380 mi apart?

Let x represent the number of hours after the first car leaves. Enter an equation that can be used to solve this problem in the first box. Solve for x and enter the number of hours in the second box.

Answer 1

recall your d = rt, distance = rate * time

thus
`\bf \begin{array}{lccclll} &distance&rate&time(hrs)\\ &-----&-----&-----\\ \textit{first car}&d&55&x\\ \textit{second car}&380-d&75&x+1 \end{array}\\\\ -----------------------------\\\\ \begin{cases} \boxed{d}=(55)(x)\\\\ 380-d=(75)(x+1)\\ ----------\\ 380-\left( \boxed{(55)(x)} \right)=(75)(x+1) \end{cases}`

notice, the first car leaves at "x" time, the other leaves on hour later, or x + 1

the first car travels some distance "d", whatever that is, thus
the second car, picks up the slack, or the difference, they're 380 miles
apart, thus the difference is 380-d