SOLUTION: A person drives 300 miles, usually at 55 mph but an accident slows her down to 15 mph. if her trip took 6 hours, how many miles did she drive at the reduced speed?

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Question 660269: A person drives 300 miles, usually at 55 mph but an accident slows her down to 15 mph. if her trip took 6 hours, how many miles did she drive at the reduced speed?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time spent driving at 15 mi/hr
+6+-+t+ = time spent driving at 55 mi/hr
Let +d+ = distance driven at 15 mi/hr
+300+-+d+ = distance driven at 55 mi/hr
--------
given:
(1) +d+=+15t+
(2) +300+-+d+=+55%2A%28+6+-+t+%29+
-------------------------
Substitute (1) into (2)
(2) +300+-+15t+=+55%2A%28+6+-+t+%29+
(2) +300+-+15t+=+330+-+55t+
(2) +55t+-+15t+=+330+-+300+
(2) +40t+=+30+
(2) +t+=+3%2F4+
and
(1) +d+=+15t+
(1) +d+=+15%2A%283%2F4%29+
(1) +d+=+45%2F4+
(1) +d+=+11.25+
She drove 11.25 mi at 15 mi/hr
check:
(2) +300+-+d+=+55%2A%28+6+-+t+%29+
(2) +300+-+11.25+=+55%2A%28+6+-+t+%29+
(2) +288.75+=+55%2A%28+6+-+t+%29+
(2) +288.75+=+330+-+55t+
(2) +55t+=+330+-+288.75+
(2) +55t+=+41.25+
(2) +t+=+.75+
(2) +t+=+3%2F4+
OK