SOLUTION: Karen notices that her husband left for the airport without his briefcase. Her husband drives 40 miles per hour and has a 15 minute head start. If Karen drives 60 miles per hour

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Question 1019878: Karen notices that her husband left for the airport without his briefcase. Her husband drives 40 miles per hour and has a 15 minute head start. If Karen drives 60 miles per hour and the airport is 45 miles away, will she catch her husband before he arrives at the airport?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
15 min is +1%2F4+ hr
Her husband's head start is:
+d%5B1%5D+=+40%2A%281%2F4%29+
+d%5B1%5D+=+10+ mi
-------------------
Let +d+ = distance Karen drives until
she catches husband
Let +t+ = time in hrs it takes
her to catch husband
Start a stopwatch when Karen leaves
-------------------
Husband's equation:
(1) +d+-+10+=+40t+
Karen's equation:
(2) +d+=+60t+
----------------
(2) +t+=+d%2F60+
and
(1) +d+-+10+=+40%2A%28+d%2F60+%29+
(1) +60d+-+600+=+40d+
(1) +20d+=+600+
(1) +d+=+30+
------------------
She catches him 30 mi from home
which is less than 45 mi, so the answer
is yes.
---------
check:
(2) +t+=+d%2F60+
(2) +t+=+30%2F60+
(2) +t+=1%2F2+
and
(1) +d+-+10+=+40t+
(1) +30+-+10+=+40t+
(1) +40t+=+20+
(1) +t+=+1%2F2+
OK