SOLUTION: Darren drives to school in rush hour traffic and averages 32mph. He returns home in mid-afternoon when there is less traffic and averages 48mph. What is the distance between his ho

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Question 897070: Darren drives to school in rush hour traffic and averages 32mph. He returns home in mid-afternoon when there is less traffic and averages 48mph. What is the distance between his home and school if the total traveling time is 1hr and 15min?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs to get from home to school
Let +d+ = distance from home to school
-----------------
Home to school equation:
(1) +d+=+32t+
School to home equation:
(2) +d+=+48%2A%28+1.25+-+t+%29+
------------------------
Substitute (1) into (2)
(2) +32t+=+60+-+48t+
(2) +80t+=+60+
(2) +t+=+3%2F4+
and
(1) +d+=+32t+
(1) +d+=+32%2A%283%2F4%29+
(1) +d+=+24+
The distance between his home and school is
24 miles
-------------
check:
(2) +d+=+48%2A%28+1.25+-+t+%29+
(2) +24+=+48%2A%28+1.25+-+.75+%29+
(2) +24+=+48%2A%28+1%2F2+%29+
(2) +24+=+24+
OK