SOLUTION: A dog chased a cat across a farm field. The dog was running at the speed of 13 m/s, while the cat was travelling at 11 m/s. The cat started the chase 16 m ahead of the dog and was

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Question 905431: A dog chased a cat across a farm field. The dog was running at the speed of 13 m/s, while the cat was travelling at 11 m/s. The cat started the chase 16 m ahead of the dog and was 77 m from the safety of an oak tree. calculate whether or not the dog caught the cat.
Found 2 solutions by ewatrrr, josmiceli:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Dog: 93m/13mpsec = 7.15sec
cat 77m/11mpsec = 7 sec
dog did not catch the cat

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The cats head start was +16+ m
Start a stop watch when the dog starts running
Let +t+ = time when the dog catches
( or does not catch ) cat depending on whether
the cat makes it to the tree
Let +d+ = distance dog runs until dog
catches cat ( or can't catch cat, because
cat is up the tree )
------------------------------------------
Dog's equation:
(1) +d+=+13t+
Cat's equation:
(2) +d+-+16+=+11t+
-------------------
Substitute (1) into (2)
(2) +13t+-+16+=+11t+
(2) +2t+=+16+
(2) +t+=+8+
and
(1) +d+=+13t+
(1) +d+=+13%2A8+
(1) +d+=+104+
-------------------
When the cat reaches the tree,
+77++=+11t%5B1%5D+
+t%5B1%5D+=+7+sec+
Since the dog needs +8+ sec
to catch the cat, The cat will be safe
-------------------------------
check:
In +7+ sec, the dog has traveled
+d%5B2%5D+=+13%2A7+
+d%5B2%5D+=+91+ m
The dog needs to +104+ m
to catch the cat, so cat is safe