SOLUTION: I need help solving this problem. It is 11:00 am when you leave point A. You stop for a 30 minute lunch break at point B, then you drive the rest of the way to your destination at

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Question 897558: I need help solving this problem. It is 11:00 am when you leave point A. You stop for a 30 minute lunch break at point B, then you drive the rest of the way to your destination at point C, which is twice the distance you drove from point A to point B. You drive at an average speed of 50 mph for the trip from point A to point B, and you drive an average of 60 mph from point B to point C. If you arrive at point C at 1:43 pm, what is the total distance you drove
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t%5B1%5D+ = the time in hrs to get from A to B
Let +d+ = the distance from A to B
Let +t%5B2%5D+ = actual time spent driving from B to C
-----------------
Equation for A to B:
+d+=+50t%5B1%5D+
Equation for B to C:
+2d+=+60t%5B2%5D+
-----------------
also,
11 AM to 1:43 PM is
+2+ hrs + +43%2F60+ hrs
+43%2F60+=+.7167+ hrs, so
+2.7167+ hrs
+t%5B1%5D+%2B+t%5B2%5D+=+2.7167+-+.5+
+t%5B1%5D+%2B+t%5B2%5D+=+2.2167+ hrs
+t%5B2%5D+=+2.2167+-+t%5B1%5D+
----------------------
+2d+=+60%2A%28+2.2167+-+t%5B1%5D+%29+
+2d+=+133+-+60t%5B1%5D+
By substitution:
+2%2A%28+50t%5B1%5D+%29+=+133+-+60t%5B1%5D+
+100t%5B1%5D+=+133+-+60t%5B1%5D+
+160t%5B1%5D+=+133+%5D%5D%5D%0D%0A%5B%5B%5B+t%5B1%5D+=+.83125+
and
+d+=+50t%5B1%5D+
+d+=+50%2A.83125+
+d+=+41.5625+
and
+2d+=+83.125+
+d+%2B+2d+=+124.6875+
You drove 124.6875 miles
check:
+t%5B2%5D+=+2.2167+-+t%5B1%5D+
+t%5B2%5D+=+2.2167+-+.83125+
+t%5B2%5D+=+1.38545+
and
+2d+=+60t%5B2%5D+
+83.125+=+60%2A1.38545+
+83.125+=+83.127+
close enough