SOLUTION: Miss Orloff drove from Hillside to Manor Haven at an average speed of 40 mph. By travelling at an average rate of 48 mph., she arrived 30 minutes earlier. How far is it from Hillsi

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Question 960403: Miss Orloff drove from Hillside to Manor Haven at an average speed of 40 mph. By travelling at an average rate of 48 mph., she arrived 30 minutes earlier. How far is it from Hillside to Manor Haven?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = distance in miles from Hillside to Manor Haven
Let +t+ = time to get there driving at +40+ mi/hr
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Equation driving at normal rate:
(1) +d+=+40t+
Equation driving at +48+ mi/hr
(2) +d+=+48%2A%28+t+-+.5+%29+
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Substitute (1) into (2)
(2) +40t+=+48%2A%28+t+-+.5+%29+
(2) +40t+=+48t+-+24+
(2) +8t+=+24+
(2) +t+=+3+
and
(1) +d+=+40%2A3+
(1) +d+=+120+
The distance is 120 mi
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check:
(2) +d+=+48%2A%28+3+-+.5+%29+
(2) +d+=+48%2A2.5+
(2) +d+=+120+
OK