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melomori [17]
3 years ago
14

Two cars leave the same location traveling in opposite directions. One car leaves at 3:00 p.m. traveling at an average rate of 5

5 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.
Mathematics
1 answer:
sergey [27]3 years ago
8 0
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
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