SOLUTION: 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

Question 62935: 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?
Found 2 solutions by joyofmath, 303795:
Answer by joyofmath(189) (Show Source): You can put this solution on YOUR website!
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?
At time t, in hours, Cameron's distance traveled = .
At time t, in hourse, Ruth's distance traveled = .
When Ruth catches up the distance traveled by the two of them is the same.
So, we solve for the two equations being equal: .
Subtrace 55t from both sides: or .
So, Ruth catches up in 1/4 hour or .
Let's verify the answer.
In 15 minutes (1/4 hour) Cameron has traveled plus the 20 miles he has as a head start. .
In 15 minutes Ruth has traveled .
Answer by 303795(602) (Show Source): You can put this solution on YOUR website!
Time (t) is measured in hours.
The distance Cameron has travelled at any time (t) = 55t + 20.
The distance Ruth has travelled at any time (t) = 135t.
They meet when they have travelled the same distance.
55t + 20 = 135t Subtract 55t from each side of the equation
55t - 55t + 20 = 135t - 55t
20 = 80 t Divide each side by 80 to get
t = 20/80 hours
ie they catch up in 1/4 of an hour or 15 minutes
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