SOLUTION: 1 Jane and Peter leave their home traveling in opposite directions on a straight road. Peter drives 15 miles per hour faster than Jane. After three hours, they are 225 miles apar

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Question 815208: 1 Jane and Peter leave their home traveling in opposite directions on a straight road. Peter drives 15 miles per hour faster than Jane. After three hours, they are 225 miles apart. Find Peter’s rate and Jane’s rate.

2 Noya drives into the city to buy a computer program. Due to traffic conditions, she averages only 15 mi/h. On her drive home, she averages 35 mi/h. If her total travel time is 2 hours, how long did it take her to drive to the computer store?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Think of this as Jane standing still and
Peter moving away from her at the sum of their speeds
Let Jane's speed in mi/hr = +s+
Peter's speed = +s+%2B+15+
----------------------
When Peter is 225 mi from Jane:
+225+=+%28+s+%2B+s+%2B+15+%29%2A3+
+225+=+%28+2s+%2B+15+%29%2A3+
+6s+%2B+45+=+225+
+6s+=+180+
+s+=+30+
+s+%2B+15+=+45+
Jane's rate is 30 mi/hr
Peter's rate is 45 mi/hr
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Average speed = ( total distance ) / ( total time )
Let +d+ = distance from home to city
+15+=+d+%2F+t%5B1%5D+
+d+=+15t%5B1%5D+ mi
------------
Going back home:
+15t%5B1%5D+=+35%2At%5B2%5D+
+3%2At%5B1%5D+=+7t%5B2%5D%0D%0A%7B%7B%7B+t%5B2%5D+=+%283%2F7%29%2At%5B1%5D+
also:
+t%5B1%5D+%2B+t%5B2%5D=+2+
By substitution:
+t%5B1%5D+%2B+%283%2F7%29%2At%5B1%5D+=+2+
+t%5B1%5D%28+7%2F7+%2B+3%2F7+%29+=+2+
+t%5B1%5D%2A%28+7+%2B+3+%29+=+14+
+t%5B1%5D+=+14%2F10+
+t%5B1%5D+=+7%2F5+
+t%5B1%5D+=+1.4+
+.4%2A60+=+24+
Her time going to the store was 1 hr 24 min