SOLUTION: Grace drove a distance of 189 miles. Part of the time she averaged 65mph and for the remaining time, she averaged 55mph. The entire trip took 3 hours? How long did she travel at ea

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Grace drove a distance of 189 miles. Part of the time she averaged 65mph and for the remaining time, she averaged 55mph. The entire trip took 3 hours? How long did she travel at ea      Log On

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Question 999782: Grace drove a distance of 189 miles. Part of the time she averaged 65mph and for the remaining time, she averaged 55mph. The entire trip took 3 hours? How long did she travel at each rate?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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M=miles at 65 mph; 189-M=miles at 55 mph
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(M/65)+(189-M)/55=3 hours
(55M/3575)+(65(189-M)/3575)=3 hours
(55M+12285-65M)/3575=3 hours
-10M+12285=10725
-10M=--1560
M=156
She drove 156 miles at 65 mph.
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156 mi/65 mph=2.4 hours
ANSWER 1: She drove 2.4 hours at 65 mph
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189-M = 189-156 = 33miles
She drove 33 miles at 55 mph
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33 mi/55 mph=0.6 hours
ANSWER 2: She drove 0.6 hours at 55 mph.
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CHECK:
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(Time at 65 mph)(65 mph)+ (Time at 55 mph)(55 mph)=189 mi
(2.4 hrs)(65 mph)+(0.06 hrs)(55 mph)=189 mi
156 mi + 33 mi = 189 mi
189 mi = 189 mi
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