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

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) (Show Source): You can put this solution on YOUR website!
.
M=miles at 65 mph; 189-M=miles at 55 mph
.
(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.
.
156 mi/65 mph=2.4 hours
ANSWER 1: She drove 2.4 hours at 65 mph
.
189-M = 189-156 = 33miles
She drove 33 miles at 55 mph
.
33 mi/55 mph=0.6 hours
ANSWER 2: She drove 0.6 hours at 55 mph.
.
CHECK:
.
(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
.
RELATED QUESTIONS
Peter drove a distance of 189 miles. Part of the time he averaged 65 miles per hour and... (answered by stanbon)

Peter drove a distance of 189 miles. Part of the time he averaged 65 miles per hour, and... (answered by josmiceli)

On the first part of a 363-mile trip, Emily averaged 58 miles per hour. Due to increased... (answered by nerdybill)

Danielle drove to a resort 260 miles from her home. She averaged 54 mph for the first... (answered by checkley79)

Carol drove to a resort 146 miles from her home. She averaged 54 mph for the first part... (answered by ewatrrr)

Jan and Kathy drove a total of 534 miles in 12.8 hours. Jan drove the first part of the... (answered by ankor@dixie-net.com)

Uniform Motion Dave and Jane drove a total of 935 miles in 15.2 hours. Dave drove the (answered by Nate)

Gillbert and Chris drove a total of 1040 miles in 17.4 hours. Gillbert drove the first... (answered by ankor@dixie-net.com)

Kathy and Jan drove a total of 497 miles in 10.4 hours. Kathy drove the first part of the (answered by checkley77)