Candice leaves on a long trip driving at a steady rate of 25 miles per hour. Her sister Liz leaves from the same location traveling to the same destination 4 hours later. She drives at a steady rate of 50 miles per hour. How long after Liz leaves home will she catch up to Candice?

Question

ranga · Answer

Let Liz catches up with Candice in x hours.

How much distance did Liz travel in x hours?

Candice left 4 hours before Liz.  So Candice travels for (x + 4) hours.

How much distance did Candice travel in (x + 4) hours?

Equate the two distances and solve for x.

jdoe0001 · Answer

$\large \begin{array}{lrlll}
&distance=&rate&time\
\hline\
candice&d=&25&x+4\
liz&d=&50&x
\end{array}\ \quad \\implies d=d\quad \textit{same distance, when they meet}$