SOLUTION: Students are traveling in two cars to a football game 135 miles away. The first car leaves on time and travels at an average speed of 45 mph. The second car starts 1/2 hour later a

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Question 157522: Students are traveling in two cars to a football game 135 miles away. The first car leaves on time and travels at an average speed of 45 mph. The second car starts 1/2 hour later and travels at an average speed of 55 miles per hour. At these speeds, how long will it take the second car of students to catch up to the first car?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If they both travel the same route, then meet at some point,
they will have both gone the same distance.
I can write 2 sets of equations with distance, d the same
for both
d+=+r%5B1%5D%2At%5B1%5D
d+=+r%5B2%5D%2At%5B2%5D
It is given that r%5B1%5D+=+45mi/hr
and also given that r%5B2%5D+=+55mi/hr
Since the 2nd car leaves 1/2 hr later that car 1,
It will have been on the road 1/2 hr less when
they meet, so t%5B2%5D+=+t%5B1%5D+-+.5
So far I have:
d+=+45%2At%5B1%5D
d+=+55%2A%28t%5B1%5D+-+.5%29
They both equal d, so I'll set them equal to eachother
45t%5B1%5D+=+55t%5B1%5D+-+27.5
10t%5B1%5D+=+27.5
t%5B1%5D+=+2.75hrs
This is how long the 1st car is on the road
The 2nd car takes 2.75+-+.5+=+2.25hrs to catch up
or 2 hrs and 15 min answer