Question 62935
<b>Cameron had driven his car 20 kilometers before Ruth began driving her car to catch up. How long will it take Ruth to catch Cameron if Cameron travels at 55 kilometers per hour and Ruth  travels at 135 kilometers per hour?</b>

At time t, in hours, Cameron's distance traveled = {{{20+55t}}}.
At time t, in hourse, Ruth's distance traveled = {{{135t}}}.

When Ruth catches up the distance traveled by the two of them is the same.
So, we solve for the two equations being equal: {{{20+55t=135t}}}.
Subtrace 55t from both sides: {{{20=80t}}} or {{{highlight(t=1/4)}}}.

So, Ruth catches up in 1/4 hour or {{{highlight(15 minutes)}}}.

Let's verify the answer.

In 15 minutes (1/4 hour) Cameron has traveled {{{(1/4)55}}} plus the 20 miles he has as a head start. {{{(1/4)55+20 = 13.75+20 = 33.75}}}.

In 15 minutes Ruth has traveled {{{(1/4)135 = 33.75}}}.